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I am a problem with solve differential equation, please help me: THANKS 

g := (y^2-1)^2; I4 := int(g^4, y = -1 .. 1); I5 := 2*(int(g^3*(diff(g, y, y)), y = -1 .. 1)); I6 := int(g^3*(diff(g, y, y, y, y)), y = -1 .. 1); with(Student[Calculus1]); I10 := ApproximateInt(6/(1-f(x)*g)^2, y = -1 .. 1, method = simpson);

dsys3 := {I4*f(x)^2*(diff(f(x), x, x, x, x))+I5*f(x)^2*(diff(f(x), x, x))+I6*f(x)^3 = I10, f(-1) = 0, f(1) = 0, ((D@@1)(f))(-1) = 0, ((D@@1)(f))(1) = 0};

dsol5 := dsolve(dsys3, numeric, output = array([0.]));

              Error, (in dsolve/numeric/bvp) system is singular at left endpoint, use midpoint method instead

****************FORMAT TWO ********************************************************

g := (y^2-1)^2; I4 := int(g^4, y = -1 .. 1); I5 := 2*(int(g^3*(diff(g, y, y)), y = -1 .. 1)); I6 := int(g^3*(diff(g, y, y, y, y)), y = -1 .. 1); with(Student[Calculus1]); I10 := ApproximateInt(6/(1-f(x)*g)^2, y = -1 .. 1, method = simpson);
dsys3 := {I4*f(x)^2*(diff(f(x), x, x, x, x))+I5*f(x)^2*(diff(f(x), x, x))+I6*f(x)^3 = I10, f(-1) = 0, f(1) = 0, ((D@@1)(f))(-1) = 0, ((D@@1)(f))(1) = 0};

dsol5 := dsolve(dsys3, method = bvp[midrich], output = array([0.]));
%;
                                   Error, (in dsolve) too many levels of recursion

I DONT KNOW ABOUT THIS ERROR

PLEASE HELP ME

THANKS A LOT

 

As am trying to solve this integration:


A(c,n,m):=evalf(int(1/(y)*exp(-c*y^(2)),y=n..m))

B(c,n,m):=evalf(int(exp(-c*y^(2)),y=n..m))

C(c,n,m):=evalf(int(y*exp(-c*y^(2)),y=n..m))

d(c,n,m):=evalf(int(y^(2)*exp(-c*y^(2)),y=n..m))

E(c,n,m):=evalf(int(y^(3)*exp(-c*y^(2)),y=n..m))

F0 := exp(beta*s1)*exp(gamma0^2*exp(beta*s1)/(2*gamma1))*A((1/2)*gamma1*exp(beta*s1), gamma0/gamma1,gamma0/gamma1+tau1)/gamma1+exp(beta*s2)*exp(gamma0^2*exp(beta*s2)/(2*gamma1))*A((1/2)*gamma1*exp(beta*s2), gamma0/gamma1+a, gamma0/gamma1+tau2-tau1+a)/gamma1+exp(beta*s3)*exp(gamma0^2*exp(beta*s3)/(2*gamma1))*A((1/2)*gamma1*exp(beta*s3), gamma0/gamma1+b, gamma0/gamma1+c-tau2+b)/gamma1

F1 := exp(beta*s1)*exp(gamma0^2*exp(beta*s1)/(2*gamma1))*(gamma0^2*A((1/2)*gamma1*exp(beta*s1), gamma0/gamma1, gamma0/gamma1+tau1)/gamma1^2-2*gamma0*B((1/2)*gamma1*exp(beta*s1), gamma0/gamma1, gamma0/gamma1+tau1)/gamma1+C((1/2)*gamma1*exp(beta*s1), gamma0/gamma1, gamma0/gamma1+tau1))/gamma1+exp(beta*s2)*exp(gamma0^2*exp(beta*s2)/(2*gamma1))*(gamma0^2*A((1/2)*gamma1*exp(beta*s2), gamma0/gamma1+a, gamma0/gamma1+tau2-tau1+a)/gamma1^2-2*gamma0*B((1/2)*gamma1*exp(beta*s2), gamma0/gamma1+a, gamma0/gamma1+tau2-tau1+a)/gamma1+C((1/2)*gamma1*exp(beta*s2), gamma0/gamma1+a, gamma0/gamma1+tau2-tau1+a))/gamma1+exp(beta*s3)*exp(gamma0^2*exp(beta*s3)/(2*gamma1))*(gamma0^2*A((1/2)*gamma1*exp(beta*s3), gamma0/gamma1+b, gamma0/gamma1+c-tau2+b)/gamma1^2-2*gamma0*B((1/2)*gamma1*exp(beta*s3), gamma0/gamma1+b, gamma0/gamma1+c-tau2+b)/gamma1+C((1/2)*gamma1*exp(beta*s3), gamma0/gamma1+b, gamma0/gamma1+c-tau2+b))/gamma1

F01 := exp(beta*s1)*exp(gamma0^2*exp(beta*s1)/(2*gamma1))*(B((1/2)*gamma1*exp(beta*s1), gamma0/gamma1, gamma0/gamma1+tau1)-gamma0*A((1/2)*gamma1*exp(beta*s1), gamma0/gamma1, gamma0/gamma1+tau1)/gamma1)/gamma1+exp(beta*s2)*exp(gamma0^2*exp(beta*s2)/(2*gamma1))*(B((1/2)*gamma1*exp(beta*s2), gamma0/gamma1+a, gamma0/gamma1+tau2-tau1+a)-gamma0*A((1/2)*gamma1*exp(beta*s2), gamma0/gamma1+a, gamma0/gamma1+tau2-tau1+a)/gamma1)/gamma1+exp(beta*s3)*exp(gamma0^2*exp(beta*s3)/(2*gamma1))*(B((1/2)*gamma1*exp(beta*s3), gamma0/gamma1+b, gamma0/gamma1+c-tau2+b)-gamma0*A((1/2)*gamma1*exp(beta*s3), gamma0/gamma1+b, gamma0/gamma1+c-tau2+b)/gamma1)/gamma1

`Fβ` := int((s1^2*(gamma0*t+(1/2)*gamma1*t^2)*exp(beta*s1)*(gamma1*t+gamma0)*exp(beta*s1))*exp(-(gamma0*t+(1/2)*gamma1*t^2)*exp(beta*s1)), t = 0 .. tau1)+int((s2^2*(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2)*exp(beta*s2)*(gamma0+gamma1*(a+t-tau1))*exp(beta*s2))*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2)*exp(beta*s2)), t = tau1 .. tau2)+int((s3^2*(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2)*exp(beta*s3)*(gamma0+gamma1*(b+t-tau2))*exp(beta*s3))*exp(-(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2)*exp(beta*s3)), t = tau2 .. c)+int((s3^2*(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2)*exp(beta*s3)*(gamma0+gamma1*(b+t-tau2))*exp(beta*s3))*exp(-(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2)*exp(beta*s3)), t = c .. infinity)

I need to have tau2 as varibles to get there optimal values ..

Minimize(1/((F0*F1-F01^2)*n^3*`Fβ`), tau2 = 237..273})

But this error keeps coming :

Error, (in Optimization:-NLPSolve) integration range or variable must be specified in the second argument, got HFloat(1.0) = 121.0828419 .. HFloat(193.0828419)

Please Help ..

When I enter the following code from the help file:

 

textplot3d([[1,2,3,"antelope", 'font'=["times","roman",20]], [3,2,1,"tiger"]], 'axes'='boxed', 'view'=[0..4, 0..4, 0..4]);

 

I receive the error message:

Plotting error, invalid FONT specification

I am trying to reduce the font size to fit many closely spaced strings in the plot.

Can anyone help.  I am running maple 16 on  Windows 7 machine.

hello, I put in the code:

> with(plots), with(ColorTools), with(LinearAlgebra), with(RandomTools), with(ExcelTools);
> A := `<|>`(`<,>`(1, 2, 0, 2, 3, 4, 3, 4, 7, 9, 5, 3, 4, 6, 7, 8, 3), `<,>`(0, 4, 7, 2, 2, 2, 4, 5, 6.5, 7, 5, 3, 2, 5, 9, 0, 1), `<,>`(1, 5, 2, 0, 4, 1, 2, 3, 4.3, 7, 8, 5, 3, 2, 9, 6, 4)); J := convert(Import("testB1.xlsx", "Cartesian", "E2:G18"), matrix);
Error, (in convert/matrix) expecting array, rtable or list
> B := matrix([[1], [.2], [.1], [.8], [.5], [.6], [.8], [.764], [.234], [0.4e-1], [.89], [.36], [.687], [.627], [.689], [.328], [.139]]); H := convert(Import("test.xlsx", "Cartesian", "D2:D18"), matrix);
Error, (in convert/matrix) expecting array, rtable or list
> C := [seq(Color([H[i, 1], 0, 0]), i = 1 .. RowDimension(A))];

 

And i get the error message everytime I try import m data list and I dont understand why. Any help would be appreciated. Thank you

 

Jennifer

hi all.

I have wrore the following program for optimization with bernstein and block pulse hybrid functions.

the program have some errors which i can't understand.

Bernestien1.mws

restart:

alias(C=binomial):
with(LinearAlgebra):
macro(LA= LinearAlgebra):


HybrFunc:=proc(N, M,  tj)               # N=Number of subintervals,  M=Number of functions in subintervals
 
local B, n, m;

global b;

for n from 1 to N do
for m from 0 to M-1 do

B := (i,m,t) -> C(m,i)*(1-t)^(m-i)*t^i:

b[n,m]:=unapply(piecewise(t>=(n-1)*tj/N and t<n*tj/N, B(m,2,N*t-(n-1)*tj), 0), t):
 od:od:


Array(1..N, 0..M-1, (n,m)->b[n,m](t)):

#convert(%,vector);
end proc:

HybrFunc(3, 3, 1);




                                       # End Of Definition
 
g2(t):=t;            #*exp(t-1):                      # Any other function can be replaced here
    

g1(t):=add(add(c[n,m]*b[n,m](t), m=0..2), n=1..3);
Optimization[Minimize](sqrt(int((g2(t)-g1(t))^2, t=0.. 1)));
assign(op(%[2]));
plot([g2(t),g1(t)], t=0..1, 0..5, color=[blue,red],thickness=[1,3],discont, scaling=constrained);

Array(1 .. 3, 0 .. 2, {(1, 0) = piecewise(0 <= t and t < 1/3, (1-3*t)^2, 0), (1, 1) = piecewise(0 <= t and t < 1/3, (6*(1-3*t))*t, 0), (1, 2) = piecewise(0 <= t and t < 1/3, 9*t^2, 0), (2, 0) = piecewise(1/3 <= t and t < 2/3, (2-3*t)^2, 0), (2, 1) = piecewise(1/3 <= t and t < 2/3, (2*(2-3*t))*(3*t-1), 0), (2, 2) = piecewise(1/3 <= t and t < 2/3, (3*t-1)^2, 0), (3, 0) = piecewise(2/3 <= t and t < 1, (3-3*t)^2, 0), (3, 1) = piecewise(2/3 <= t and t < 1, (2*(3-3*t))*(3*t-2), 0), (3, 2) = piecewise(2/3 <= t and t < 1, (3*t-2)^2, 0)}, datatype = anything, storage = rectangular, order = Fortran_order)

g2(t) := t

"g1(t):=c[1,0] ({[[(1-3 t)^2,0<=t and t<1/3],[0,otherwise]])+c[1,1] ({[[6 (1-3 t) t,0<=t and t<1/3],[0,otherwise]])+c[1,2] ({[[9 t^2,0<=t and t<1/3],[0,otherwise]])+c[2,0] ({[[(2-3 t)^2,1/3<=t and t<2/3],[0,otherwise]])+c[2,1] ({[[2 (2-3 t) (3 t-1),1/3<=t and t<2/3],[0,otherwise]])+c[2,2] ({[[(3 t-1)^2,1/3<=t and t<2/3],[0,otherwise]])+c[3,0] ({[[(3-3 t)^2,2/3<=t and t<1],[0,otherwise]])+c[3,1] ({[[2 (3-3 t) (3 t-2),2/3<=t and t<1],[0,otherwise]])+c[3,2] ({[[(3 t-2)^2,2/3<=t and t<1],[0,otherwise]])"

Error, (in Optimization:-NLPSolve) complex value encountered

Error, invalid left hand side in assignment

(1)



Download Bernestien1.mws

 I'll be so grateful if any one can help me.

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

Pleaz i nees help i have probleme withe singularity

restart; with(plots)

Paramétres

 

NULL

``

mb := 5;

5

 

2

 

(1/3)*a*b^3

 

0.4906250000e-1*d

 

.2

 

.4

 

1.2

 

.43

 

9.81

 

1

 

5

 

.5

 

1

(1.1)

``

``

Equation suivant x :

 

``

eq1 := (mp+mb)*(diff(x(t), `$`(t, 2)))+mp*(d+l)*(diff(theta(t), `$`(t, 2)))+mp*l*(diff(alpha(t), `$`(t, 2)))+mp*(d*(diff(theta(t), t))^2*theta(t)+l*(diff(theta(t), t)+diff(alpha(t), t))^2*(alpha(t)+theta(t)))+1000*Am*g*sin(omega*t-k*x(t))*(1+theta(t))*(sinh(k*(h+z(t)-(1/2)*a*theta(t)+(1/2)*b))-sinh(k*(h+z(t)+(1/2)*a*theta(t)+(1/2)*b)))/cosh(k*h) = 0;

7*(diff(diff(x(t), t), t))+1.2*(diff(diff(theta(t), t), t))+.4*(diff(diff(alpha(t), t), t))+.8*(diff(theta(t), t))^2*theta(t)+.4*(diff(theta(t), t)+diff(alpha(t), t))^2*(alpha(t)+theta(t))+11772.000*sin(.43*t-x(t))*(1+theta(t))*(-sinh(-11/2-z(t)+.2500000000*theta(t))-sinh(11/2+z(t)+.2500000000*theta(t)))/cosh(5) = 0

(2.1)

``

Equation suivant z :

 

``

eq2 := (mp+mb)*(diff(z(t), `$`(t, 2)))-mp*(l*(alpha(t)+theta(t))+d*theta(t))*(diff(theta(t), `$`(t, 2)))-mp*l*(alpha(t)+theta(t))*(diff(alpha(t), `$`(t, 2)))+mp*(d*(diff(theta(t), t))^2+l*(diff(theta(t), t)+diff(alpha(t), t))^2)-g*(mp+mb)+1000*g*a*z(t)+1000*g*a*b*(1/2)+1000*Am*g*sin(omega*t-k*x(t))*(1-theta(t))*(sinh(k*(h+z(t)-(1/2)*a*theta(t)+(1/2)*b))-sin(k*(h+z(t)+(1/2)*a*theta(t)+(1/2)*b)))/cosh(k*h) = 0;

7*(diff(diff(z(t), t), t))-2*(.2*alpha(t)+.6*theta(t))*(diff(diff(theta(t), t), t))-.4*(alpha(t)+theta(t))*(diff(diff(alpha(t), t), t))+.8*(diff(theta(t), t))^2+.4*(diff(theta(t), t)+diff(alpha(t), t))^2+2383.830+4905.000*z(t)+11772.000*sin(.43*t-x(t))*(1-theta(t))*(-sinh(-11/2-z(t)+.2500000000*theta(t))-sin(11/2+z(t)+.2500000000*theta(t)))/cosh(5) = 0

(3.1)

``

Equation suivant y :

 

``

eq3 := mp*(d+l)*(diff(x(t), `$`(t, 2)))-mp*(l*(alpha(t)+theta(t))+d*theta(t))*(diff(z(t), `$`(t, 2)))+(Ip+Ib+mp*(d^2+l^2)+2*mp*d*l)*(diff(theta(t), `$`(t, 2)))+(Ip+mp*l^2+mp*d*l*cos(alpha(t)))*(diff(alpha(t), `$`(t, 2)))-mp*alpha(t)*(l*d*(diff(theta(t), t))^2-l*d*(diff(theta(t), t)+diff(alpha(t), t))^2)+mp*g*l*(alpha(t)+theta(t))+mp*g*d*theta(t)+1000*g*a*theta(t)*z(t)^2+1000*g*a*b*theta(t)*z(t)+1000*g*a(theta(t))^9*(1/12)+(1000*g*a*b^2*(1/4))*theta(t)-1000*Am*g*sin(omega*t-k*x(t))*((z(t)-(1/2)*a*theta(t)+(1/2)*b)*sinh(k*(h+z(t)-(1/2)*a*theta(t)+(1/2)*b))/k-cosh(k*(h+z(t)-(1/2)*a*theta(t)+(1/2)*b))/k^2)/cosh(k*h)+1000*Am*g*sin(omega*t-k*x(t))*((z(t)+(1/2)*a*theta(t)+(1/2)*b)*sinh(k*(h+z(t)+(1/2)*a*theta(t)+(1/2)*b))/k-cosh(k*(h+z(t)+(1/2)*a*theta(t)+(1/2)*b))/k^2)/cosh(k*h)-(1000*g*z(t)*(1/2)+1000*g*b*(1/4))*(2*a*x(t)+a*b*theta(t))+1000*g*a*theta(t)*z(t)^2+1000*g*a*b*theta(t)^2*z(t)+(1000*g*a^3*(1/12))*theta(t)+(1000*g*a*b^2*(1/4))*theta(t)^3+(k*theta(t)*(x(t)-(1/2)*a+(1/2)*b*theta(t))*sinh(k*(h+z(t)+(1/2)*b-theta(t)*(x(t)-(1/2)*a+(1/2)*b*theta(t))))-k*theta(t)*(x(t)+(1/2)*a+(1/2)*b*theta(t))*sinh(k*(h+z(t)+(1/2)*b-theta(t)*(x(t)+(1/2)*a+(1/2)*b*theta(t))))-cosh(k*(h+z(t)+(1/2)*b-theta(t)*(x(t)+(1/2)*a+(1/2)*b*theta(t))))+cosh(k*(h+z(t)+(1/2)*b-theta(t)*(x(t)-(1/2)*a+(1/2)*b*theta(t)))))/k^2 = 0;

1.2*(diff(diff(x(t), t), t))-2*(.2*alpha(t)+.6*theta(t))*(diff(diff(z(t), t), t))+.9062916667*(diff(diff(theta(t), t), t))+(0.9962500000e-1+.16*cos(alpha(t)))*(diff(diff(alpha(t), t), t))-2*alpha(t)*(0.8e-1*(diff(theta(t), t))^2-0.8e-1*(diff(theta(t), t)+diff(alpha(t), t))^2)+3.924*alpha(t)+1340.209500*theta(t)+9810.000*theta(t)*z(t)^2+4905.000*theta(t)*z(t)+1.596679687-11772.000*sin(.43*t-x(t))*(-(z(t)-.2500000000*theta(t)+1/2)*sinh(-11/2-z(t)+.2500000000*theta(t))-cosh(-11/2-z(t)+.2500000000*theta(t)))/cosh(5)+11772.000*sin(.43*t-x(t))*((z(t)+.2500000000*theta(t)+1/2)*sinh(11/2+z(t)+.2500000000*theta(t))-cosh(11/2+z(t)+.2500000000*theta(t)))/cosh(5)-(4905.00*z(t)+2452.50)*(1.0*x(t)+.5*theta(t))+4905.000*theta(t)^2*z(t)+1226.250*theta(t)^3-theta(t)*(x(t)-.2500000000+(1/2)*theta(t))*sinh(-11/2-z(t)+theta(t)*(x(t)-.2500000000+(1/2)*theta(t)))+theta(t)*(x(t)+.2500000000+(1/2)*theta(t))*sinh(-11/2-z(t)+theta(t)*(x(t)+.2500000000+(1/2)*theta(t)))-cosh(-11/2-z(t)+theta(t)*(x(t)+.2500000000+(1/2)*theta(t)))+cosh(-11/2-z(t)+theta(t)*(x(t)-.2500000000+(1/2)*theta(t))) = 0

(4.1)

NULL

``

Equation suivant y

 

``

eq4 := mp*l*(diff(x(t), `$`(t, 2)))-mp*l*(alpha(t)+theta(t))*(diff(z(t), `$`(t, 2)))+(d*l*mp+l^2*mp+Ip)*(diff(theta(t), `$`(t, 2)))+(l^2*mp+Ip)*(diff(alpha(t), `$`(t, 2)))-9.81*mp*l*(alpha(t)+theta(t))-l*d*mp*(diff(theta(t), `$`(t, 1)))^2*alpha(t) = 0;

.4*(diff(diff(x(t), t), t))-.4*(alpha(t)+theta(t))*(diff(diff(z(t), t), t))+.2596250000*(diff(diff(theta(t), t), t))+0.9962500000e-1*(diff(diff(alpha(t), t), t))-3.924*alpha(t)-3.924*theta(t)-.16*(diff(theta(t), t))^2*alpha(t) = 0

(5.1)

``

Résolution :

 

NULL

CI:= x(0)=0,z(0)=0,theta(0)=0,alpha(0)=0,D(x)(0)=0,D(alpha)(0)=0,D(z)(0)=0,D(theta)(0)=0;

x(0) = 0, z(0) = 0, theta(0) = 0, alpha(0) = 0, (D(x))(0) = 0, (D(alpha))(0) = 0, (D(z))(0) = 0, (D(theta))(0) = 0

(6.1)

if theta(t) <> 0 then
 solution:=dsolve([eq1,eq2,eq3,eq4,CI],numeric,maxfun=0):
 odeplot(solution, [[t, x(t)]], t = 0 .. 100, thickness = 2);
 odeplot(solution, [[t, z(t)]], t = 0 .. 100, thickness = 2);
 odeplot(solution, [[t, theta(t)]], t = 0 .. 100, thickness = 2);
 odeplot(solution, [[t, alpha(t)]], t = 0 .. 100, thickness = 2);
 #odeplot(solution,[[t,x(t)],[t,alpha(t)],[t,z(t)],[t,theta(t)]], t=0..100, thickness=2);
 end ;

proc (x_rkf45) local _res, _dat, _vars, _solnproc, _xout, _ndsol, _pars, _n, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](x_rkf45) else _xout := evalf(x_rkf45) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _dtbl, _dat, _vmap, _x0, _y0, _val, _dig, _n, _ne, _nd, _nv, _pars, _ini, _par, _i, _j, _k, _src; option `Copyright (c) 2002 by Waterloo Maple Inc. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _pars := []; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 20, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = 0.14822202628077855e-4, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 4 ) = (Array(1..53, {(1) = 8, (2) = 8, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 1, (19) = 0, (20) = 0, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0}, datatype = integer[4])), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 6 ) = (Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = alpha(t), Y[2] = diff(alpha(t),t), Y[3] = theta(t), Y[4] = diff(theta(t),t), Y[5] = x(t), Y[6] = diff(x(t),t), Y[7] = z(t), Y[8] = diff(z(t),t)]`; YP[2] := -(-14.947516474811375000+9.3616250000*cosh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-9.3616250000*cosh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))-12681.242976943909200*Y[3]-171.4392330064092*Y[1]-11479.6926562500000*Y[3]^3+9.3616250000*Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))-9.3616250000*Y[3]*(Y[5]+.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))+7*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])*(-2*Y[1]*(0.8e-1*Y[4]^2-0.8e-1*(Y[4]+Y[2])^2)+3.924*Y[1]+1340.209500*Y[3]+9810.000*Y[3]*Y[7]^2+4905.000*Y[3]*Y[7]+1.596679687-158.631022309198*sin(.43*X-Y[5])*(-(Y[7]-.2500000000*Y[3]+1/2)*sinh(-11/2-Y[7]+.2500000000*Y[3])-cosh(-11/2-Y[7]+.2500000000*Y[3]))+158.631022309198*sin(.43*X-Y[5])*((Y[7]+.2500000000*Y[3]+1/2)*sinh(11/2+Y[7]+.2500000000*Y[3])-cosh(11/2+Y[7]+.2500000000*Y[3]))-(4905.00*Y[7]+2452.50)*(1.0*Y[5]+.5*Y[3])+4905.000*Y[3]^2*Y[7]+1226.250*Y[3]^3-Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-cosh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))+cosh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])))-56.5942610739837*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3]))-1.2*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])-4.9040416669*(-.4*Y[1]-.4*Y[3])*(.8*Y[4]^2+.4*(Y[4]+Y[2])^2+2383.830+4905.000*Y[7]+158.631022309198*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3])))+1.3373750000*(.8*Y[4]^2+.4*(Y[4]+Y[2])^2+2383.830+4905.000*Y[7]+158.631022309198*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-1.2*Y[3])-.285413333408*Y[4]^2*Y[3]-.142706666704*(Y[4]+Y[2])^2*(Y[1]+Y[3])+.4*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-1.2*Y[3])^2-1485.04414422534*sin(.43*X-Y[5])*((Y[7]+.2500000000*Y[3]+1/2)*sinh(11/2+Y[7]+.2500000000*Y[3])-cosh(11/2+Y[7]+.2500000000*Y[3]))+1485.04414422534*sin(.43*X-Y[5])*(-(Y[7]-.2500000000*Y[3]+1/2)*sinh(-11/2-Y[7]+.2500000000*Y[3])-cosh(-11/2-Y[7]+.2500000000*Y[3]))-5.492526666928*Y[4]^2*Y[1]-7*(-3.924*Y[1]-3.924*Y[3]-.16*Y[4]^2*Y[1])*(-.4*Y[1]-1.2*Y[3])^2+18.7232500000*Y[1]*(0.8e-1*Y[4]^2-0.8e-1*(Y[4]+Y[2])^2)-91837.5412500000000*Y[3]*Y[7]^2-45918.7706250000000*Y[3]*Y[7]+9.3616250000*(4905.00*Y[7]+2452.50)*(1.0*Y[5]+.5*Y[3])-45918.7706250000000*Y[3]^2*Y[7])/(2.3445975001253875000-.53737500000*(-.4*Y[1]-1.2*Y[3])^2+.8573750000*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])-1.497860000000*cos(Y[1])-4.9040416669*(-.4*Y[1]-.4*Y[3])^2+7*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])*(0.9962500000e-1+.16*cos(Y[1]))); YP[4] := (-6.0061102276113750000+3.76162500000*cosh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-3.76162500000*cosh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))-5028.1809204375000000*Y[3]-1.57597650000000*Y[1]-4612.69265625000000*Y[3]^3+3.76162500000*Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))-3.76162500000*Y[3]*(Y[5]+.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-7*(-.4*Y[1]-.4*Y[3])*(.8*Y[4]^2+.4*(Y[4]+Y[2])^2+2383.830+4905.000*Y[7]+158.631022309198*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3])))*(0.9962500000e-1+.16*cos(Y[1]))-7*(-3.924*Y[1]-3.924*Y[3]-.16*Y[4]^2*Y[1])*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])+132.750371019452*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3]))+.4*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])+.48*(-.4*Y[1]-.4*Y[3])*(.8*Y[4]^2+.4*(Y[4]+Y[2])^2+2383.830+4905.000*Y[7]+158.631022309198*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3])))+7*(-.4*Y[1]-.4*Y[3])^2*(-2*Y[1]*(0.8e-1*Y[4]^2-0.8e-1*(Y[4]+Y[2])^2)+3.924*Y[1]+1340.209500*Y[3]+9810.000*Y[3]*Y[7]^2+4905.000*Y[3]*Y[7]+1.596679687-158.631022309198*sin(.43*X-Y[5])*(-(Y[7]-.2500000000*Y[3]+1/2)*sinh(-11/2-Y[7]+.2500000000*Y[3])-cosh(-11/2-Y[7]+.2500000000*Y[3]))+158.631022309198*sin(.43*X-Y[5])*((Y[7]+.2500000000*Y[3]+1/2)*sinh(11/2+Y[7]+.2500000000*Y[3])-cosh(11/2+Y[7]+.2500000000*Y[3]))-(4905.00*Y[7]+2452.50)*(1.0*Y[5]+.5*Y[3])+4905.000*Y[3]^2*Y[7]+1226.250*Y[3]^3-Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-cosh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))+cosh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])))-2.8*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(0.9962500000e-1+.16*cos(Y[1]))+49*(-3.924*Y[1]-3.924*Y[3]-.16*Y[4]^2*Y[1])*(0.9962500000e-1+.16*cos(Y[1]))-1.2*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-.4*Y[3])^2+.53737500000*(.8*Y[4]^2+.4*(Y[4]+Y[2])^2+2383.830+4905.000*Y[7]+158.631022309198*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-1.2*Y[3])+.6694800000000*Y[4]^2*Y[3]+.3347400000000*(Y[4]+Y[2])^2*(Y[1]+Y[3])-596.710419293836*sin(.43*X-Y[5])*((Y[7]+.2500000000*Y[3]+1/2)*sinh(11/2+Y[7]+.2500000000*Y[3])-cosh(11/2+Y[7]+.2500000000*Y[3]))+596.710419293836*sin(.43*X-Y[5])*(-(Y[7]-.2500000000*Y[3]+1/2)*sinh(-11/2-Y[7]+.2500000000*Y[3])-cosh(-11/2-Y[7]+.2500000000*Y[3]))+.5376*Y[4]^2*Y[1]+7.52325000000*Y[1]*(0.8e-1*Y[4]^2-0.8e-1*(Y[4]+Y[2])^2)-36901.54125000000000*Y[3]*Y[7]^2-18450.77062500000000*Y[3]*Y[7]+3.76162500000*(4905.00*Y[7]+2452.50)*(1.0*Y[5]+.5*Y[3])-18450.77062500000000*Y[3]^2*Y[7])/(2.3445975001253875000-.53737500000*(-.4*Y[1]-1.2*Y[3])^2+.8573750000*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])-1.497860000000*cos(Y[1])-4.9040416669*(-.4*Y[1]-.4*Y[3])^2+7*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])*(0.9962500000e-1+.16*cos(Y[1]))); YP[6] := -(-.1754750976013000000+.109900000000*cosh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-.109900000000*cosh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))-137.33141624963376000*Y[3]+9.526360200366240*Y[1]-134.764875000000000*Y[3]^3+.109900000000*Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))-.109900000000*Y[3]*(Y[5]+.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-.4*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])*(-2*Y[1]*(0.8e-1*Y[4]^2-0.8e-1*(Y[4]+Y[2])^2)+3.924*Y[1]+1340.209500*Y[3]+9810.000*Y[3]*Y[7]^2+4905.000*Y[3]*Y[7]+1.596679687-158.631022309198*sin(.43*X-Y[5])*(-(Y[7]-.2500000000*Y[3]+1/2)*sinh(-11/2-Y[7]+.2500000000*Y[3])-cosh(-11/2-Y[7]+.2500000000*Y[3]))+158.631022309198*sin(.43*X-Y[5])*((Y[7]+.2500000000*Y[3]+1/2)*sinh(11/2+Y[7]+.2500000000*Y[3])-cosh(11/2+Y[7]+.2500000000*Y[3]))-(4905.00*Y[7]+2452.50)*(1.0*Y[5]+.5*Y[3])+4905.000*Y[3]^2*Y[7]+1226.250*Y[3]^3-Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-cosh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))+cosh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])))-1.2*(-.4*Y[1]-.4*Y[3])*(.8*Y[4]^2+.4*(Y[4]+Y[2])^2+2383.830+4905.000*Y[7]+158.631022309198*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3])))*(0.9962500000e-1+.16*cos(Y[1]))-1.2*(-3.924*Y[1]-3.924*Y[3]-.16*Y[4]^2*Y[1])*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])+100.258795838552*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3]))+.2596250000*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])+(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])*(0.9962500000e-1+.16*cos(Y[1]))+.36251666668*(-.4*Y[1]-.4*Y[3])*(.8*Y[4]^2+.4*(Y[4]+Y[2])^2+2383.830+4905.000*Y[7]+158.631022309198*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3])))+1.2*(-.4*Y[1]-.4*Y[3])^2*(-2*Y[1]*(0.8e-1*Y[4]^2-0.8e-1*(Y[4]+Y[2])^2)+3.924*Y[1]+1340.209500*Y[3]+9810.000*Y[3]*Y[7]^2+4905.000*Y[3]*Y[7]+1.596679687-158.631022309198*sin(.43*X-Y[5])*(-(Y[7]-.2500000000*Y[3]+1/2)*sinh(-11/2-Y[7]+.2500000000*Y[3])-cosh(-11/2-Y[7]+.2500000000*Y[3]))+158.631022309198*sin(.43*X-Y[5])*((Y[7]+.2500000000*Y[3]+1/2)*sinh(11/2+Y[7]+.2500000000*Y[3])-cosh(11/2+Y[7]+.2500000000*Y[3]))-(4905.00*Y[7]+2452.50)*(1.0*Y[5]+.5*Y[3])+4905.000*Y[3]^2*Y[7]+1226.250*Y[3]^3-Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-cosh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))+cosh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])))-1.8173750000*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(0.9962500000e-1+.16*cos(Y[1]))+8.4*(-3.924*Y[1]-3.924*Y[3]-.16*Y[4]^2*Y[1])*(0.9962500000e-1+.16*cos(Y[1]))-.9062916667*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-.4*Y[3])^2+0.15700000000e-1*(.8*Y[4]^2+.4*(Y[4]+Y[2])^2+2383.830+4905.000*Y[7]+158.631022309198*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-1.2*Y[3])+.50562012085193000000*Y[4]^2*Y[3]+.25281006042596500000*(Y[4]+Y[2])^2*(Y[1]+Y[3])-0.9962500000e-1*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-1.2*Y[3])^2-17.4335493517808*sin(.43*X-Y[5])*((Y[7]+.2500000000*Y[3]+1/2)*sinh(11/2+Y[7]+.2500000000*Y[3])-cosh(11/2+Y[7]+.2500000000*Y[3]))+17.4335493517808*sin(.43*X-Y[5])*(-(Y[7]-.2500000000*Y[3]+1/2)*sinh(-11/2-Y[7]+.2500000000*Y[3])-cosh(-11/2-Y[7]+.2500000000*Y[3]))+.4060186666816*Y[4]^2*Y[1]+.4*(-3.924*Y[1]-3.924*Y[3]-.16*Y[4]^2*Y[1])*(-.4*Y[1]-1.2*Y[3])^2+.219800000000*Y[1]*(0.8e-1*Y[4]^2-0.8e-1*(Y[4]+Y[2])^2)-1078.119000000000000*Y[3]*Y[7]^2-539.059500000000000*Y[3]*Y[7]+.109900000000*(4905.00*Y[7]+2452.50)*(1.0*Y[5]+.5*Y[3])-539.059500000000000*Y[3]^2*Y[7])/(2.3445975001253875000-.53737500000*(-.4*Y[1]-1.2*Y[3])^2+.8573750000*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])-1.497860000000*cos(Y[1])-4.9040416669*(-.4*Y[1]-.4*Y[3])^2+7*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])*(0.9962500000e-1+.16*cos(Y[1]))); YP[8] := -(-.53737500000*(-.4*Y[1]-1.2*Y[3])*(-2*Y[1]*(0.8e-1*Y[4]^2-0.8e-1*(Y[4]+Y[2])^2)+3.924*Y[1]+1340.209500*Y[3]+9810.000*Y[3]*Y[7]^2+4905.000*Y[3]*Y[7]+1.596679687-158.631022309198*sin(.43*X-Y[5])*(-(Y[7]-.2500000000*Y[3]+1/2)*sinh(-11/2-Y[7]+.2500000000*Y[3])-cosh(-11/2-Y[7]+.2500000000*Y[3]))+158.631022309198*sin(.43*X-Y[5])*((Y[7]+.2500000000*Y[3]+1/2)*sinh(11/2+Y[7]+.2500000000*Y[3])-cosh(11/2+Y[7]+.2500000000*Y[3]))-(4905.00*Y[7]+2452.50)*(1.0*Y[5]+.5*Y[3])+4905.000*Y[3]^2*Y[7]+1226.250*Y[3]^3-Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-cosh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))+cosh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])))-.48*(-3.924*Y[1]-3.924*Y[3]-.16*Y[4]^2*Y[1])*(-.4*Y[1]-1.2*Y[3])+1.3373750000*(-.4*Y[1]-.4*Y[3])*(-2*Y[1]*(0.8e-1*Y[4]^2-0.8e-1*(Y[4]+Y[2])^2)+3.924*Y[1]+1340.209500*Y[3]+9810.000*Y[3]*Y[7]^2+4905.000*Y[3]*Y[7]+1.596679687-158.631022309198*sin(.43*X-Y[5])*(-(Y[7]-.2500000000*Y[3]+1/2)*sinh(-11/2-Y[7]+.2500000000*Y[3])-cosh(-11/2-Y[7]+.2500000000*Y[3]))+158.631022309198*sin(.43*X-Y[5])*((Y[7]+.2500000000*Y[3]+1/2)*sinh(11/2+Y[7]+.2500000000*Y[3])-cosh(11/2+Y[7]+.2500000000*Y[3]))-(4905.00*Y[7]+2452.50)*(1.0*Y[5]+.5*Y[3])+4905.000*Y[3]^2*Y[7]+1226.250*Y[3]^3-Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-cosh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))+cosh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])))-4.9040416669*(-3.924*Y[1]-3.924*Y[3]-.16*Y[4]^2*Y[1])*(-.4*Y[1]-.4*Y[3])+.119550000000*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-1.2*Y[3])+7*(-3.924*Y[1]-3.924*Y[3]-.16*Y[4]^2*Y[1])*(-.4*Y[1]-1.2*Y[3])*(0.9962500000e-1+.16*cos(Y[1]))-.4*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-1.2*Y[3])*(0.9962500000e-1+.16*cos(Y[1]))+74.2676316024185*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3]))+1116.0579164503566049-1.3373750000*(.8*Y[4]^2+.4*(Y[4]+Y[2])^2+2383.830+4905.000*Y[7]+158.631022309198*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3])))*(0.9962500000e-1+.16*cos(Y[1]))+0.5096666668e-1*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-.4*Y[3])+2296.4154659472358125*Y[7]+.37454278751433000000*Y[4]^2+.18727139375716500000*(Y[4]+Y[2])^2)/(2.3445975001253875000-.53737500000*(-.4*Y[1]-1.2*Y[3])^2+.8573750000*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])-1.497860000000*cos(Y[1])-4.9040416669*(-.4*Y[1]-.4*Y[3])^2+7*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])*(0.9962500000e-1+.16*cos(Y[1]))); YP[1] := Y[2]; YP[3] := Y[4]; YP[5] := Y[6]; YP[7] := Y[8]; 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 11 ) = (Array(1..6, 0..8, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0}, datatype = float[8], order = C_order)), ( 8 ) = ([Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = 17.65307013401197, (3) = .0, (4) = -7.093237546136753, (5) = .0, (6) = .20723671453704962, (7) = .0, (8) = -340.5471428571427}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..8, {(1) = .1, (2) = .1, (3) = .1, (4) = .1, (5) = .1, (6) = .1, (7) = .1, (8) = .1}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, 1..8, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0}, datatype = float[8], order = C_order), Array(1..8, 1..8, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0}, datatype = float[8], order = C_order), Array(1..8, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0}, datatype = integer[4]), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order)]), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 13 ) = (), ( 12 ) = (), ( 20 ) = ([]), ( 16 ) = ([0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = alpha(t), Y[2] = diff(alpha(t),t), Y[3] = theta(t), Y[4] = diff(theta(t),t), Y[5] = x(t), Y[6] = diff(x(t),t), Y[7] = z(t), Y[8] = diff(z(t),t)]`; YP[2] := -(-14.947516474811375000+9.3616250000*cosh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-9.3616250000*cosh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))-12681.242976943909200*Y[3]-171.4392330064092*Y[1]-11479.6926562500000*Y[3]^3+9.3616250000*Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))-9.3616250000*Y[3]*(Y[5]+.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))+7*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])*(-2*Y[1]*(0.8e-1*Y[4]^2-0.8e-1*(Y[4]+Y[2])^2)+3.924*Y[1]+1340.209500*Y[3]+9810.000*Y[3]*Y[7]^2+4905.000*Y[3]*Y[7]+1.596679687-158.631022309198*sin(.43*X-Y[5])*(-(Y[7]-.2500000000*Y[3]+1/2)*sinh(-11/2-Y[7]+.2500000000*Y[3])-cosh(-11/2-Y[7]+.2500000000*Y[3]))+158.631022309198*sin(.43*X-Y[5])*((Y[7]+.2500000000*Y[3]+1/2)*sinh(11/2+Y[7]+.2500000000*Y[3])-cosh(11/2+Y[7]+.2500000000*Y[3]))-(4905.00*Y[7]+2452.50)*(1.0*Y[5]+.5*Y[3])+4905.000*Y[3]^2*Y[7]+1226.250*Y[3]^3-Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-cosh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))+cosh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])))-56.5942610739837*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3]))-1.2*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])-4.9040416669*(-.4*Y[1]-.4*Y[3])*(.8*Y[4]^2+.4*(Y[4]+Y[2])^2+2383.830+4905.000*Y[7]+158.631022309198*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3])))+1.3373750000*(.8*Y[4]^2+.4*(Y[4]+Y[2])^2+2383.830+4905.000*Y[7]+158.631022309198*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-1.2*Y[3])-.285413333408*Y[4]^2*Y[3]-.142706666704*(Y[4]+Y[2])^2*(Y[1]+Y[3])+.4*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-1.2*Y[3])^2-1485.04414422534*sin(.43*X-Y[5])*((Y[7]+.2500000000*Y[3]+1/2)*sinh(11/2+Y[7]+.2500000000*Y[3])-cosh(11/2+Y[7]+.2500000000*Y[3]))+1485.04414422534*sin(.43*X-Y[5])*(-(Y[7]-.2500000000*Y[3]+1/2)*sinh(-11/2-Y[7]+.2500000000*Y[3])-cosh(-11/2-Y[7]+.2500000000*Y[3]))-5.492526666928*Y[4]^2*Y[1]-7*(-3.924*Y[1]-3.924*Y[3]-.16*Y[4]^2*Y[1])*(-.4*Y[1]-1.2*Y[3])^2+18.7232500000*Y[1]*(0.8e-1*Y[4]^2-0.8e-1*(Y[4]+Y[2])^2)-91837.5412500000000*Y[3]*Y[7]^2-45918.7706250000000*Y[3]*Y[7]+9.3616250000*(4905.00*Y[7]+2452.50)*(1.0*Y[5]+.5*Y[3])-45918.7706250000000*Y[3]^2*Y[7])/(2.3445975001253875000-.53737500000*(-.4*Y[1]-1.2*Y[3])^2+.8573750000*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])-1.497860000000*cos(Y[1])-4.9040416669*(-.4*Y[1]-.4*Y[3])^2+7*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])*(0.9962500000e-1+.16*cos(Y[1]))); YP[4] := (-6.0061102276113750000+3.76162500000*cosh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-3.76162500000*cosh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))-5028.1809204375000000*Y[3]-1.57597650000000*Y[1]-4612.69265625000000*Y[3]^3+3.76162500000*Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))-3.76162500000*Y[3]*(Y[5]+.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-7*(-.4*Y[1]-.4*Y[3])*(.8*Y[4]^2+.4*(Y[4]+Y[2])^2+2383.830+4905.000*Y[7]+158.631022309198*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3])))*(0.9962500000e-1+.16*cos(Y[1]))-7*(-3.924*Y[1]-3.924*Y[3]-.16*Y[4]^2*Y[1])*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])+132.750371019452*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3]))+.4*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])+.48*(-.4*Y[1]-.4*Y[3])*(.8*Y[4]^2+.4*(Y[4]+Y[2])^2+2383.830+4905.000*Y[7]+158.631022309198*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3])))+7*(-.4*Y[1]-.4*Y[3])^2*(-2*Y[1]*(0.8e-1*Y[4]^2-0.8e-1*(Y[4]+Y[2])^2)+3.924*Y[1]+1340.209500*Y[3]+9810.000*Y[3]*Y[7]^2+4905.000*Y[3]*Y[7]+1.596679687-158.631022309198*sin(.43*X-Y[5])*(-(Y[7]-.2500000000*Y[3]+1/2)*sinh(-11/2-Y[7]+.2500000000*Y[3])-cosh(-11/2-Y[7]+.2500000000*Y[3]))+158.631022309198*sin(.43*X-Y[5])*((Y[7]+.2500000000*Y[3]+1/2)*sinh(11/2+Y[7]+.2500000000*Y[3])-cosh(11/2+Y[7]+.2500000000*Y[3]))-(4905.00*Y[7]+2452.50)*(1.0*Y[5]+.5*Y[3])+4905.000*Y[3]^2*Y[7]+1226.250*Y[3]^3-Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-cosh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))+cosh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])))-2.8*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(0.9962500000e-1+.16*cos(Y[1]))+49*(-3.924*Y[1]-3.924*Y[3]-.16*Y[4]^2*Y[1])*(0.9962500000e-1+.16*cos(Y[1]))-1.2*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-.4*Y[3])^2+.53737500000*(.8*Y[4]^2+.4*(Y[4]+Y[2])^2+2383.830+4905.000*Y[7]+158.631022309198*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-1.2*Y[3])+.6694800000000*Y[4]^2*Y[3]+.3347400000000*(Y[4]+Y[2])^2*(Y[1]+Y[3])-596.710419293836*sin(.43*X-Y[5])*((Y[7]+.2500000000*Y[3]+1/2)*sinh(11/2+Y[7]+.2500000000*Y[3])-cosh(11/2+Y[7]+.2500000000*Y[3]))+596.710419293836*sin(.43*X-Y[5])*(-(Y[7]-.2500000000*Y[3]+1/2)*sinh(-11/2-Y[7]+.2500000000*Y[3])-cosh(-11/2-Y[7]+.2500000000*Y[3]))+.5376*Y[4]^2*Y[1]+7.52325000000*Y[1]*(0.8e-1*Y[4]^2-0.8e-1*(Y[4]+Y[2])^2)-36901.54125000000000*Y[3]*Y[7]^2-18450.77062500000000*Y[3]*Y[7]+3.76162500000*(4905.00*Y[7]+2452.50)*(1.0*Y[5]+.5*Y[3])-18450.77062500000000*Y[3]^2*Y[7])/(2.3445975001253875000-.53737500000*(-.4*Y[1]-1.2*Y[3])^2+.8573750000*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])-1.497860000000*cos(Y[1])-4.9040416669*(-.4*Y[1]-.4*Y[3])^2+7*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])*(0.9962500000e-1+.16*cos(Y[1]))); YP[6] := -(-.1754750976013000000+.109900000000*cosh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-.109900000000*cosh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))-137.33141624963376000*Y[3]+9.526360200366240*Y[1]-134.764875000000000*Y[3]^3+.109900000000*Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))-.109900000000*Y[3]*(Y[5]+.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-.4*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])*(-2*Y[1]*(0.8e-1*Y[4]^2-0.8e-1*(Y[4]+Y[2])^2)+3.924*Y[1]+1340.209500*Y[3]+9810.000*Y[3]*Y[7]^2+4905.000*Y[3]*Y[7]+1.596679687-158.631022309198*sin(.43*X-Y[5])*(-(Y[7]-.2500000000*Y[3]+1/2)*sinh(-11/2-Y[7]+.2500000000*Y[3])-cosh(-11/2-Y[7]+.2500000000*Y[3]))+158.631022309198*sin(.43*X-Y[5])*((Y[7]+.2500000000*Y[3]+1/2)*sinh(11/2+Y[7]+.2500000000*Y[3])-cosh(11/2+Y[7]+.2500000000*Y[3]))-(4905.00*Y[7]+2452.50)*(1.0*Y[5]+.5*Y[3])+4905.000*Y[3]^2*Y[7]+1226.250*Y[3]^3-Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-cosh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))+cosh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])))-1.2*(-.4*Y[1]-.4*Y[3])*(.8*Y[4]^2+.4*(Y[4]+Y[2])^2+2383.830+4905.000*Y[7]+158.631022309198*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3])))*(0.9962500000e-1+.16*cos(Y[1]))-1.2*(-3.924*Y[1]-3.924*Y[3]-.16*Y[4]^2*Y[1])*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])+100.258795838552*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3]))+.2596250000*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])+(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])*(0.9962500000e-1+.16*cos(Y[1]))+.36251666668*(-.4*Y[1]-.4*Y[3])*(.8*Y[4]^2+.4*(Y[4]+Y[2])^2+2383.830+4905.000*Y[7]+158.631022309198*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3])))+1.2*(-.4*Y[1]-.4*Y[3])^2*(-2*Y[1]*(0.8e-1*Y[4]^2-0.8e-1*(Y[4]+Y[2])^2)+3.924*Y[1]+1340.209500*Y[3]+9810.000*Y[3]*Y[7]^2+4905.000*Y[3]*Y[7]+1.596679687-158.631022309198*sin(.43*X-Y[5])*(-(Y[7]-.2500000000*Y[3]+1/2)*sinh(-11/2-Y[7]+.2500000000*Y[3])-cosh(-11/2-Y[7]+.2500000000*Y[3]))+158.631022309198*sin(.43*X-Y[5])*((Y[7]+.2500000000*Y[3]+1/2)*sinh(11/2+Y[7]+.2500000000*Y[3])-cosh(11/2+Y[7]+.2500000000*Y[3]))-(4905.00*Y[7]+2452.50)*(1.0*Y[5]+.5*Y[3])+4905.000*Y[3]^2*Y[7]+1226.250*Y[3]^3-Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-cosh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))+cosh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])))-1.8173750000*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(0.9962500000e-1+.16*cos(Y[1]))+8.4*(-3.924*Y[1]-3.924*Y[3]-.16*Y[4]^2*Y[1])*(0.9962500000e-1+.16*cos(Y[1]))-.9062916667*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-.4*Y[3])^2+0.15700000000e-1*(.8*Y[4]^2+.4*(Y[4]+Y[2])^2+2383.830+4905.000*Y[7]+158.631022309198*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-1.2*Y[3])+.50562012085193000000*Y[4]^2*Y[3]+.25281006042596500000*(Y[4]+Y[2])^2*(Y[1]+Y[3])-0.9962500000e-1*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-1.2*Y[3])^2-17.4335493517808*sin(.43*X-Y[5])*((Y[7]+.2500000000*Y[3]+1/2)*sinh(11/2+Y[7]+.2500000000*Y[3])-cosh(11/2+Y[7]+.2500000000*Y[3]))+17.4335493517808*sin(.43*X-Y[5])*(-(Y[7]-.2500000000*Y[3]+1/2)*sinh(-11/2-Y[7]+.2500000000*Y[3])-cosh(-11/2-Y[7]+.2500000000*Y[3]))+.4060186666816*Y[4]^2*Y[1]+.4*(-3.924*Y[1]-3.924*Y[3]-.16*Y[4]^2*Y[1])*(-.4*Y[1]-1.2*Y[3])^2+.219800000000*Y[1]*(0.8e-1*Y[4]^2-0.8e-1*(Y[4]+Y[2])^2)-1078.119000000000000*Y[3]*Y[7]^2-539.059500000000000*Y[3]*Y[7]+.109900000000*(4905.00*Y[7]+2452.50)*(1.0*Y[5]+.5*Y[3])-539.059500000000000*Y[3]^2*Y[7])/(2.3445975001253875000-.53737500000*(-.4*Y[1]-1.2*Y[3])^2+.8573750000*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])-1.497860000000*cos(Y[1])-4.9040416669*(-.4*Y[1]-.4*Y[3])^2+7*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])*(0.9962500000e-1+.16*cos(Y[1]))); YP[8] := -(-.53737500000*(-.4*Y[1]-1.2*Y[3])*(-2*Y[1]*(0.8e-1*Y[4]^2-0.8e-1*(Y[4]+Y[2])^2)+3.924*Y[1]+1340.209500*Y[3]+9810.000*Y[3]*Y[7]^2+4905.000*Y[3]*Y[7]+1.596679687-158.631022309198*sin(.43*X-Y[5])*(-(Y[7]-.2500000000*Y[3]+1/2)*sinh(-11/2-Y[7]+.2500000000*Y[3])-cosh(-11/2-Y[7]+.2500000000*Y[3]))+158.631022309198*sin(.43*X-Y[5])*((Y[7]+.2500000000*Y[3]+1/2)*sinh(11/2+Y[7]+.2500000000*Y[3])-cosh(11/2+Y[7]+.2500000000*Y[3]))-(4905.00*Y[7]+2452.50)*(1.0*Y[5]+.5*Y[3])+4905.000*Y[3]^2*Y[7]+1226.250*Y[3]^3-Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-cosh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))+cosh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])))-.48*(-3.924*Y[1]-3.924*Y[3]-.16*Y[4]^2*Y[1])*(-.4*Y[1]-1.2*Y[3])+1.3373750000*(-.4*Y[1]-.4*Y[3])*(-2*Y[1]*(0.8e-1*Y[4]^2-0.8e-1*(Y[4]+Y[2])^2)+3.924*Y[1]+1340.209500*Y[3]+9810.000*Y[3]*Y[7]^2+4905.000*Y[3]*Y[7]+1.596679687-158.631022309198*sin(.43*X-Y[5])*(-(Y[7]-.2500000000*Y[3]+1/2)*sinh(-11/2-Y[7]+.2500000000*Y[3])-cosh(-11/2-Y[7]+.2500000000*Y[3]))+158.631022309198*sin(.43*X-Y[5])*((Y[7]+.2500000000*Y[3]+1/2)*sinh(11/2+Y[7]+.2500000000*Y[3])-cosh(11/2+Y[7]+.2500000000*Y[3]))-(4905.00*Y[7]+2452.50)*(1.0*Y[5]+.5*Y[3])+4905.000*Y[3]^2*Y[7]+1226.250*Y[3]^3-Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3]))+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3])*sinh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))-cosh(-11/2-Y[7]+Y[3]*(Y[5]+.2500000000+(1/2)*Y[3]))+cosh(-11/2-Y[7]+Y[3]*(Y[5]-.2500000000+(1/2)*Y[3])))-4.9040416669*(-3.924*Y[1]-3.924*Y[3]-.16*Y[4]^2*Y[1])*(-.4*Y[1]-.4*Y[3])+.119550000000*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-1.2*Y[3])+7*(-3.924*Y[1]-3.924*Y[3]-.16*Y[4]^2*Y[1])*(-.4*Y[1]-1.2*Y[3])*(0.9962500000e-1+.16*cos(Y[1]))-.4*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-1.2*Y[3])*(0.9962500000e-1+.16*cos(Y[1]))+74.2676316024185*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3]))+1116.0579164503566049-1.3373750000*(.8*Y[4]^2+.4*(Y[4]+Y[2])^2+2383.830+4905.000*Y[7]+158.631022309198*sin(.43*X-Y[5])*(1-Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sin(11/2+Y[7]+.2500000000*Y[3])))*(0.9962500000e-1+.16*cos(Y[1]))+0.5096666668e-1*(.8*Y[4]^2*Y[3]+.4*(Y[4]+Y[2])^2*(Y[1]+Y[3])+158.631022309198*sin(.43*X-Y[5])*(1+Y[3])*(-sinh(-11/2-Y[7]+.2500000000*Y[3])-sinh(11/2+Y[7]+.2500000000*Y[3])))*(-.4*Y[1]-.4*Y[3])+2296.4154659472358125*Y[7]+.37454278751433000000*Y[4]^2+.18727139375716500000*(Y[4]+Y[2])^2)/(2.3445975001253875000-.53737500000*(-.4*Y[1]-1.2*Y[3])^2+.8573750000*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])-1.497860000000*cos(Y[1])-4.9040416669*(-.4*Y[1]-.4*Y[3])^2+7*(-.4*Y[1]-.4*Y[3])*(-.4*Y[1]-1.2*Y[3])*(0.9962500000e-1+.16*cos(Y[1]))); YP[1] := Y[2]; YP[3] := Y[4]; YP[5] := Y[6]; YP[7] := Y[8]; 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 18 ) = ([]), ( 19 ) = (0)  ] ))  ] ); _y0 := Array(0..8, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0., (7) = 0., (8) = 0.}); _vmap := array( 1 .. 8, [( 1 ) = (1), ( 2 ) = (2), ( 3 ) = (3), ( 5 ) = (5), ( 4 ) = (4), ( 7 ) = (7), ( 6 ) = (6), ( 8 ) = (8)  ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); if _par <> [] then `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) end if; `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 10 and 10 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 10 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 10 and 10 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 10 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-10 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-10; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch:  end try else try procname(procname("right")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch:  end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 10 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error  end try; if _src = 0 and 10 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif 10 < _dat[4][9] then if _dat[4][9]-10 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-10, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif 10 < _dat[4][9] then if _dat[4][9]-10 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-10, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; _dat[4][26] := _EnvDSNumericSaveDigits; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(0..0, {}), (3) = [t, alpha(t), diff(alpha(t), t), theta(t), diff(theta(t), t), x(t), diff(x(t), t), z(t), diff(z(t), t)], (4) = []}); _vars := _dat[3]; _pars := map(rhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_rkf45, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_rkf45, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_rkf45, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_rkf45, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_rkf45), 'string') = rhs(x_rkf45); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_rkf45), 'string') = rhs(x_rkf45)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_rkf45) else _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_rkf45) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error  end try end proc

 

Warning, cannot evaluate the solution further right of .33009777, probably a singularity

 

 

 

``

``


thank you !

Download DL.mw

Why does MapletViewer launch the Maplet Splash Screen and then pop up a box saying it has an error launching the Maplet spash screen? As my previous question stated, it also will not run the maplet, popping up another error box as "explanation".

My maplet runs perfectly correctly and as expected when I run it directly from the worksheet.

However, when I export the worksheet to a .maplet file, it will not run and only gives the error:
At line 135, syntax error: reserved words `quit`, `done`, or `stop` unexpected.

According to wordpad, line 135 of the .maplet file is the last line of both the .maplet file and of the worksheet. It contains the statement:

Maplet[Display](<maplet name>);

There are no `quit`, `done`, or `stop` words anywhere visibly in the worksheet.

What is happening and how do I get the maplet to run?

******************************************where d1 to d45 -kappa and chi are constant**********

dsys4 := {d1*h1(theta)+d2*(diff(h1(theta), theta, theta))+d3*(diff(h2(theta), theta))+d4*(diff(h2(theta), theta, theta, theta))+d5*h3(theta)+d6*(diff(h3(theta), theta, theta))+d7*(diff(h1(theta), theta, theta, theta, theta)) = 0, d8*h2(theta)+d9*(diff(h2(theta), theta, theta, theta, theta))+d10*(diff(h2(theta), theta, theta))+d11*(diff(h1(theta), theta))+d12*(diff(h1(theta), theta, theta, theta))+d13*(diff(h3(theta), theta))+d14*(diff(h3(theta), theta, theta, theta)) = 0, h3(theta)^5*(d16+ln(h3(theta))^2*d15+2*ln(h3(theta))*d17)+(diff(h3(theta), theta, theta))*h3(theta)^4*(d19+ln(h3(theta))^2*d18+2*ln(h3(theta))*d20)+(diff(h3(theta), theta, theta, theta, theta))*h3(theta)^4*(d22+ln(h3(theta))^2*d21+2*ln(h3(theta))*d23)+h1(theta)*h3(theta)^4*(d25+ln(h3(theta))^2*d24+2*ln(h3(theta))*d26)+(diff(h1(theta), theta, theta))*h3(theta)^4*(d28+ln(h3(theta))^2*d27+2*ln(h3(theta))*d29)+(diff(h2(theta), theta))*h3(theta)^4*(d31+ln(h3(theta))^2*d30+2*ln(h3(theta))*d32)+(diff(h2(theta), theta, theta, theta))*h3(theta)^4*(d34+ln(h3(theta))^2*d33+2*ln(h3(theta))*d35)+h3(theta)^4*(d37+ln(h3(theta))^2*d36+2*ln(h3(theta))*d38)+h3(theta)^4*(diff(h2(theta), theta, theta, theta, theta, theta, theta))*(d40+ln(h3(theta))^2*d39+2*ln(h3(theta))*d41)-beta*h3(theta)^3*d42-chi*ln(h3(theta))^2*d43/kappa-chi*d45/kappa-2*chi*ln(h3(theta))*d44/kappa = 0, h1(0) = 0, h1(1) = 0, h2(0) = 0, h2(1) = 0, h3(0) = 1, h3(1) = 1, ((D@@1)(h1))(0) = 0, ((D@@1)(h1))(1) = 0, ((D@@1)(h2))(0) = 0, ((D@@1)(h2))(1) = 0, ((D@@1)(h3))(0) = 0, ((D@@1)(h3))(1) = 0, ((D@@2)(h3))(0) = 0, ((D@@2)(h3))(1) = 0}; dsol6 := dsolve(dsys4, 'maxmesh' = 600, numeric, output = listprocedure)

pde system solve ...

June 28 2014 wo0olf 15

hi ,

 

i solve my odes with ode analyzer and obtained h(t) , u(t) and s(t) ... i wana put u(t) and s(t) in another equation to obtain T(t,r) , i did as follow but i have an error :

 

400*(s(t)*(diff(T(t, r), r))+u(t)*(diff(T(t, r), t))/r) = 0.3e-1*((diff(T(t, r), r)+r*(diff(T(t, t), r, r)))/r+(diff(T(t, r), r))/r^2)+0.1e-2*(2*((diff(u(t), t))/r+s(t)/r)^2+((diff(s(t), t))/r-u(t)/r)^2)

 

4.00000000000000*u(t)^2*h(t)*(diff(y(t), t))-8.00000000000000*h(t)^2*x(t)^2+16.0000000000000*u(t)*h(t)*x(t)*(diff(h(t), t))+(1367.18750000000*(-29.8200000000000+u(t)))*h(t)^2*x(t)+363.281250000000*u(t)*h(t)*y(t)-1367.18750000000*h(t)^2*(30-u(t))*x(t)+u(t)^2*h(t)-0.225000000000000e-1+0.225000000000000e-1*(0.749297072727423e-1+1.49578322716831*sin(t-0.75e-1))^2+4.00000000000000*(u(t)*y(t)+h(t)*x(t))^2 = 0

 

diff(s(t), t) = 8.00000000000000*(diff(x(t), t))*h(t)+16.0000000000000*y(t)*x(t)+8.00000000000000*u(t)*(diff(y(t), t))

 

diff(h(t), t) = y(t)

 

diff(u(t), t) = x(t)

 

x(t) = 427.2460938*u(t)+385620.1174/u(t)-25671.38673

 

h(0) = 0.1e-10, s(0) = .6, u(0) = .62, x(0) = 596561.43714, y(0) = .12096, T(0, r) = 0, t = 0 .. .18, r = 0 .. .125

 

pdsolve(1, 2, 3, 4, 5, 6, {7}, numeric);
%;
Error, (in pdsolve) invalid input: `pdsolve/numeric` expects its 2nd argument, IBCs, to be of type {list, set}, but received 2

 Hi all,

i want to solve a system of differential equations in maple with "dsolve, numeric",

i got th error message: "Error, (in f) unable to store in Matrix ..."

what is the problem?

thanks a lot

I have a big expression with multiple terms. The expression is kind of :

expr = a*ln(u) + b*ln(u) + a*ln(v)+b*ln(v)

I want to factor ln(u) and ln(v) to get (a+b)*ln(u) + (a+b)*ln(v)

I tried factor(expr,ln(u)) but I get the error :
Error, (in factor) 2nd argument, ln(2*da+(4*da^2+4*d^2-4*da*Sigma[a]+Sigma[a]^2+Delta[b]^2)^(1/2)-Sigma[a]), is not a valid algebraic extension.

I tried without Delta[b] and Sigma[a] : deltab and sigmaa but it didn't work either.

Do you have an idea how to factor the many ln ?

Thanks,
Mathieu

I'm having some trouble maybe someone can point out my error please. I'm using the Maple 18 worksheet to try some basic linear equations. The trouble is in the last step.

 

1.) I start with 2 ordered pairs (2, 14) and (14,18)

Then I put in my formula to discover the slope. I confirm it looks correct in the Variables window.

m := (y2-y1)/(x2-x1);

 

2.)  Next I input the values for my ordered pairs. I also confirm thru the Variables window.

x1 := 2;

y1 := 14;

x2 := 3;

y2 := 18;

 

3.) Now I can type m and expect to get an answer to what my slope is.

m;

4.) Now I want Slope/Intercept form of y=mx+b. When I put in the formula y-y1=m(x-x1) i get a strange result

 

When I execute this formula, the result is y-14=4. (or thru context menu I tell it to solve for y, then I get y=18)

y-y1=m(x-x1) 

When I manually input the values, the output is y-14=4x-8 (or thru context menu I tell it to solve for y, then I get y=4x+6)

y-14 = 4*(x-2)

 

 

 

Why is my equation (y-y1=m(x-x1)) not executing properly?

hello evreybody i have these Error :

restart:with(plots):
M:=765 : m:=587 :I:=76.3*10^3 :Jp:=7.3*10^3 :e:=10.92: F:=0.42: omega:=0.56 :ka:=0.1:kb:=0.1:kc:=0.1: lambda1:=0.1 :lambda2:=0.1:lambda3:=0.1:
Error, illegal use of an object as a name

 

please help 
thank you !

 Hello everybody, I need help please   

 


restart:with(plots):

mb:=765; mp:=587;Ib:=76.3*10^3;Ip:=7.3*10^3; l:=0.92; d:=10; F:=-1.2; omega:=0.43;g:=9.81;ly:=3;k:=0.02001014429;

765

 

587

 

76300.0

 

7300.0

 

.92

 

10

 

-1.2

 

.43

 

9.81

 

3

 

0.2001014429e-1

(1)

A:=168913.8672;

168913.8672

(2)

s:=0.0666666666667;

0.666666666667e-1

(3)

n:=49.97465213;

49.97465213

(4)

eq1:=(mp+mb)*diff(x(t),t$2)+mp*(d*cos(theta(t))+l*cos(alpha(t)+theta(t)))*diff(theta(t),t$2)+mp*l*cos(alpha(t)+theta(t))*diff(alpha(t),t$2)+mp*(d*diff(theta(t),t)^2*sin(theta(t))+l*(diff(theta(t),t)+diff(alpha(t),t))^2*sin(alpha(t)+theta(t)))+A*2*(s*sinh(k*ly+k*ly)*sin(omega*t-k*x(t)))=0;

1352*(diff(diff(x(t), t), t))+587*(10*cos(theta(t))+.92*cos(alpha(t)+theta(t)))*(diff(diff(theta(t), t), t))+540.04*cos(alpha(t)+theta(t))*(diff(diff(alpha(t), t), t))+5870*(diff(theta(t), t))^2*sin(theta(t))+540.04*(diff(theta(t), t)+diff(alpha(t), t))^2*sin(alpha(t)+theta(t))+2710.493534*sin(.43*t-0.2001014429e-1*x(t)) = 0

(5)

eq2:=(mp+mb)*diff(z(t),t$2)-mp*d*(sin(theta(t)+alpha(t))+sin(theta(t)))*diff(theta(t),t$2)-mp*l*sin(alpha(t)+theta(t))*diff(alpha(t),t$2)+mp*(d*diff(theta(t),t)^2*cos(theta(t))+l*(diff(theta(t),t)+diff(alpha(t),t))^2*cos(alpha(t)+theta(t)))+9.81*(mp+mb)+1000*g*z(t)*15.3*30+A*cosh(k*ly+k*z(t))*n*(cos(omega*t-k*15)-cos(omega*t+k*15))=0;

1352*(diff(diff(z(t), t), t))-5870*(sin(alpha(t)+theta(t))+sin(theta(t)))*(diff(diff(theta(t), t), t))-540.04*sin(alpha(t)+theta(t))*(diff(diff(alpha(t), t), t))+5870*(diff(theta(t), t))^2*cos(theta(t))+540.04*(diff(theta(t), t)+diff(alpha(t), t))^2*cos(alpha(t)+theta(t))+13263.12+4502790.000*z(t)+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*z(t))*(cos(.43*t-.3001521644)-cos(.43*t+.3001521644)) = 0

(6)

eq3:=mp*(d*cos(theta(t))+l*cos(alpha(t)+theta(t)))*diff(x(t),t$2)-mp*(l*sin(theta(t)+alpha(t))+d*sin(theta(t)))*diff(z(t),t$2)+(Ip+Ib+mp*(d^2+l^2)+2*mp*d*l*cos(alpha(t)))*diff(theta(t),t$2)+(Ip+mp*l^2+mp*d*l*cos(alpha(t)))*diff(alpha(t),t$2)-mp*sin(alpha(t))*(l*d*diff(alpha(t),t)^2-l*d*(diff(alpha(t),t)+diff(theta(t),t))^2)+mp*9.81*l*sin(alpha(t)+theta(t))+mp*9.81*d*sin(theta(t))=0;

587*(10*cos(theta(t))+.92*cos(alpha(t)+theta(t)))*(diff(diff(x(t), t), t))-587*(.92*sin(alpha(t)+theta(t))+10*sin(theta(t)))*(diff(diff(z(t), t), t))+(142796.8368+10800.80*cos(alpha(t)))*(diff(diff(theta(t), t), t))+(7796.8368+5400.40*cos(alpha(t)))*(diff(diff(alpha(t), t), t))-587*sin(alpha(t))*(9.20*(diff(alpha(t), t))^2-9.20*(diff(theta(t), t)+diff(alpha(t), t))^2)+5297.7924*sin(alpha(t)+theta(t))+57584.70*sin(theta(t)) = 0

(7)

eq4:=mp*l*cos(alpha(t)+theta(t))*diff(x(t),t$2)-mp*l*sin(alpha(t)+theta(t))*diff(z(t),t$2)+(Ip+mp*l^2+mp*d*l*cos(alpha(t)))*diff(theta(t),t$2)+(Ip+mp*l^2)*diff(alpha(t),t$2)-mp*9.81*l*sin(alpha(t)+theta(t))+l*d*mp*diff(theta(t),t$1)^2*sin(alpha(t))=0;

540.04*cos(alpha(t)+theta(t))*(diff(diff(x(t), t), t))-540.04*sin(alpha(t)+theta(t))*(diff(diff(z(t), t), t))+(7796.8368+5400.40*cos(alpha(t)))*(diff(diff(theta(t), t), t))+7796.8368*(diff(diff(alpha(t), t), t))-5297.7924*sin(alpha(t)+theta(t))+5400.40*(diff(theta(t), t))^2*sin(alpha(t)) = 0

(8)

CI:= x(0)=0,z(0)=0,theta(0)=0,alpha(0)=0,D(x)(0)=0,D(alpha)(0)=0,D(z)(0)=0,D(theta)(0)=0;

x(0) = 0, z(0) = 0, theta(0) = 0, alpha(0) = 0, (D(x))(0) = 0, (D(alpha))(0) = 0, (D(z))(0) = 0, (D(theta))(0) = 0

(9)

solution:=dsolve([eq1,eq2,eq3,eq4,CI],numeric,maxfun=100000);

proc (x_rkf45) local _res, _dat, _vars, _solnproc, _xout, _ndsol, _pars, _n, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](x_rkf45) else _xout := evalf(x_rkf45) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _dtbl, _dat, _vmap, _x0, _y0, _val, _dig, _n, _ne, _nd, _nv, _pars, _ini, _par, _i, _j, _k, _src; option `Copyright (c) 2002 by Waterloo Maple Inc. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _pars := []; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 20, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = 0.5145421769461311e-3, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 4 ) = (Array(1..53, {(1) = 8, (2) = 8, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 1, (19) = 100000, (20) = 0, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0}, datatype = integer[4])), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 6 ) = (Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = alpha(t), Y[2] = diff(alpha(t),t), Y[3] = theta(t), Y[4] = diff(theta(t),t), Y[5] = x(t), Y[6] = diff(x(t),t), Y[7] = z(t), Y[8] = diff(z(t),t)]`; YP[2] := (540.04*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*cos(Y[1]+Y[3])*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))-730134.08*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*cos(Y[1]+Y[3])*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))+540.04*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2*sin(Y[1]+Y[3])*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))+1352*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))-1352*(7796.8368+5400.40*cos(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))+1827904*(7796.8368+5400.40*cos(Y[1]))*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))-730134.08*sin(Y[1]+Y[3])*(142796.8368+10800.80*cos(Y[1]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))+730134.08*sin(Y[1]+Y[3])*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-1827904*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(142796.8368+10800.80*cos(Y[1]))+1352*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-1352*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*(7796.8368+5400.40*cos(Y[1]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))+730134.08*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*cos(Y[1]+Y[3])*(142796.8368+10800.80*cos(Y[1]))-540.04*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*cos(Y[1]+Y[3])*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-540.04*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*sin(Y[1]+Y[3])*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3])))/(1460268.16*cos(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))-394301608.5632*cos(Y[1]+Y[3])^2*(142796.8368+10800.80*cos(Y[1]))+291643.2016*cos(Y[1]+Y[3])^2*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+291643.2016*cos(Y[1]+Y[3])*sin(Y[1]+Y[3])*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-10541323.3536*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2+291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*cos(Y[1]+Y[3])*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])+291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2*sin(Y[1]+Y[3])^2+2035121836544224.7506+153931588575265.01376*cos(Y[1])-10541323.3536*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-1827904*(7796.8368+5400.40*cos(Y[1]))^2-730134.08*(7796.8368+5400.40*cos(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])-730134.08*sin(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-394301608.5632*sin(Y[1]+Y[3])^2*(142796.8368+10800.80*cos(Y[1]))); YP[4] := -(291643.2016*cos(Y[1]+Y[3])^2*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))-394301608.5632*cos(Y[1]+Y[3])^2*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))+291643.2016*cos(Y[1]+Y[3])*sin(Y[1]+Y[3])*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))+730134.08*cos(Y[1]+Y[3])*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))-10541323.3536*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))-8365847205177.4464*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+75503444196167.489249*sin(Y[1]+Y[3])+820689610827907.49184*sin(Y[3])-730134.08*sin(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))-394301608.5632*sin(Y[1]+Y[3])^2*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))-1827904*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(7796.8368+5400.40*cos(Y[1]))-730134.08*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])-10541323.3536*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))+730134.08*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*cos(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))+291643.2016*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*cos(Y[1]+Y[3])*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])+291643.2016*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*sin(Y[1]+Y[3])^2*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3])))/(1460268.16*cos(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))-394301608.5632*cos(Y[1]+Y[3])^2*(142796.8368+10800.80*cos(Y[1]))+291643.2016*cos(Y[1]+Y[3])^2*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+291643.2016*cos(Y[1]+Y[3])*sin(Y[1]+Y[3])*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-10541323.3536*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2+291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*cos(Y[1]+Y[3])*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])+291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2*sin(Y[1]+Y[3])^2+2035121836544224.7506+153931588575265.01376*cos(Y[1])-10541323.3536*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-1827904*(7796.8368+5400.40*cos(Y[1]))^2-730134.08*(7796.8368+5400.40*cos(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])-730134.08*sin(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-394301608.5632*sin(Y[1]+Y[3])^2*(142796.8368+10800.80*cos(Y[1]))); YP[6] := (540.04*cos(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))-730134.08*cos(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))+291643.2016*cos(Y[1]+Y[3])*sin(Y[1]+Y[3])*(142796.8368+10800.80*cos(Y[1]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))-291643.2016*cos(Y[1]+Y[3])*sin(Y[1]+Y[3])*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+730134.08*cos(Y[1]+Y[3])*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(142796.8368+10800.80*cos(Y[1]))-540.04*cos(Y[1]+Y[3])*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-7796.8368*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))+10541323.3536*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))-540.04*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*sin(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))-291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*sin(Y[1]+Y[3])^2*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))-1352*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(7796.8368+5400.40*cos(Y[1]))-540.04*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])-10541323.3536*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*(142796.8368+10800.80*cos(Y[1]))+7796.8368*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+1352*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*(7796.8368+5400.40*cos(Y[1]))^2+540.04*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*(7796.8368+5400.40*cos(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])+540.04*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*sin(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+291643.2016*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*sin(Y[1]+Y[3])^2*(142796.8368+10800.80*cos(Y[1])))/(1460268.16*cos(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))-394301608.5632*cos(Y[1]+Y[3])^2*(142796.8368+10800.80*cos(Y[1]))+291643.2016*cos(Y[1]+Y[3])^2*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+291643.2016*cos(Y[1]+Y[3])*sin(Y[1]+Y[3])*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-10541323.3536*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2+291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*cos(Y[1]+Y[3])*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])+291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2*sin(Y[1]+Y[3])^2+2035121836544224.7506+153931588575265.01376*cos(Y[1])-10541323.3536*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-1827904*(7796.8368+5400.40*cos(Y[1]))^2-730134.08*(7796.8368+5400.40*cos(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])-730134.08*sin(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-394301608.5632*sin(Y[1]+Y[3])^2*(142796.8368+10800.80*cos(Y[1]))); YP[8] := -(291643.2016*cos(Y[1]+Y[3])^2*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-540.04*cos(Y[1]+Y[3])*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+1080.08*cos(Y[1]+Y[3])*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))*(7796.8368+5400.40*cos(Y[1]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))-291643.2016*cos(Y[1]+Y[3])^2*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))*(142796.8368+10800.80*cos(Y[1]))-730134.08*sin(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))+730134.08*sin(Y[1]+Y[3])*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(142796.8368+10800.80*cos(Y[1]))-7796.8368*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2+10541323.3536*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))*(142796.8368+10800.80*cos(Y[1]))-1352*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))*(7796.8368+5400.40*cos(Y[1]))^2+540.04*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*sin(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))-291643.2016*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*sin(Y[1]+Y[3])*cos(Y[1]+Y[3])*(142796.8368+10800.80*cos(Y[1]))+291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*cos(Y[1]+Y[3])*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))*sin(Y[1]+Y[3])-540.04*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*sin(Y[1]+Y[3])-10541323.3536*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+1352*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(7796.8368+5400.40*cos(Y[1]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+7796.8368*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-540.04*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*cos(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3])))/(1460268.16*cos(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))-394301608.5632*cos(Y[1]+Y[3])^2*(142796.8368+10800.80*cos(Y[1]))+291643.2016*cos(Y[1]+Y[3])^2*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+291643.2016*cos(Y[1]+Y[3])*sin(Y[1]+Y[3])*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-10541323.3536*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2+291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*cos(Y[1]+Y[3])*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])+291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2*sin(Y[1]+Y[3])^2+2035121836544224.7506+153931588575265.01376*cos(Y[1])-10541323.3536*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-1827904*(7796.8368+5400.40*cos(Y[1]))^2-730134.08*(7796.8368+5400.40*cos(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])-730134.08*sin(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-394301608.5632*sin(Y[1]+Y[3])^2*(142796.8368+10800.80*cos(Y[1]))); YP[1] := Y[2]; YP[3] := Y[4]; YP[5] := Y[6]; YP[7] := Y[8]; 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 11 ) = (Array(1..6, 0..8, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0}, datatype = float[8], order = C_order)), ( 8 ) = ([Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = -.0, (5) = .0, (6) = .0, (7) = .0, (8) = -9.809999999999999}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..8, {(1) = .1, (2) = .1, (3) = .1, (4) = .1, (5) = .1, (6) = .1, (7) = .1, (8) = .1}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, 1..8, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0}, datatype = float[8], order = C_order), Array(1..8, 1..8, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0}, datatype = float[8], order = C_order), Array(1..8, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0}, datatype = integer[4]), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order)]), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 13 ) = (), ( 12 ) = (), ( 20 ) = ([]), ( 16 ) = ([0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = alpha(t), Y[2] = diff(alpha(t),t), Y[3] = theta(t), Y[4] = diff(theta(t),t), Y[5] = x(t), Y[6] = diff(x(t),t), Y[7] = z(t), Y[8] = diff(z(t),t)]`; YP[2] := (540.04*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*cos(Y[1]+Y[3])*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))-730134.08*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*cos(Y[1]+Y[3])*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))+540.04*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2*sin(Y[1]+Y[3])*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))+1352*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))-1352*(7796.8368+5400.40*cos(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))+1827904*(7796.8368+5400.40*cos(Y[1]))*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))-730134.08*sin(Y[1]+Y[3])*(142796.8368+10800.80*cos(Y[1]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))+730134.08*sin(Y[1]+Y[3])*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-1827904*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(142796.8368+10800.80*cos(Y[1]))+1352*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-1352*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*(7796.8368+5400.40*cos(Y[1]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))+730134.08*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*cos(Y[1]+Y[3])*(142796.8368+10800.80*cos(Y[1]))-540.04*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*cos(Y[1]+Y[3])*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-540.04*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*sin(Y[1]+Y[3])*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3])))/(1460268.16*cos(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))-394301608.5632*cos(Y[1]+Y[3])^2*(142796.8368+10800.80*cos(Y[1]))+291643.2016*cos(Y[1]+Y[3])^2*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+291643.2016*cos(Y[1]+Y[3])*sin(Y[1]+Y[3])*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-10541323.3536*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2+291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*cos(Y[1]+Y[3])*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])+291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2*sin(Y[1]+Y[3])^2+2035121836544224.7506+153931588575265.01376*cos(Y[1])-10541323.3536*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-1827904*(7796.8368+5400.40*cos(Y[1]))^2-730134.08*(7796.8368+5400.40*cos(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])-730134.08*sin(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-394301608.5632*sin(Y[1]+Y[3])^2*(142796.8368+10800.80*cos(Y[1]))); YP[4] := -(291643.2016*cos(Y[1]+Y[3])^2*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))-394301608.5632*cos(Y[1]+Y[3])^2*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))+291643.2016*cos(Y[1]+Y[3])*sin(Y[1]+Y[3])*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))+730134.08*cos(Y[1]+Y[3])*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))-10541323.3536*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))-8365847205177.4464*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+75503444196167.489249*sin(Y[1]+Y[3])+820689610827907.49184*sin(Y[3])-730134.08*sin(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))-394301608.5632*sin(Y[1]+Y[3])^2*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))-1827904*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(7796.8368+5400.40*cos(Y[1]))-730134.08*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])-10541323.3536*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))+730134.08*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*cos(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))+291643.2016*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*cos(Y[1]+Y[3])*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])+291643.2016*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*sin(Y[1]+Y[3])^2*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3])))/(1460268.16*cos(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))-394301608.5632*cos(Y[1]+Y[3])^2*(142796.8368+10800.80*cos(Y[1]))+291643.2016*cos(Y[1]+Y[3])^2*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+291643.2016*cos(Y[1]+Y[3])*sin(Y[1]+Y[3])*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-10541323.3536*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2+291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*cos(Y[1]+Y[3])*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])+291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2*sin(Y[1]+Y[3])^2+2035121836544224.7506+153931588575265.01376*cos(Y[1])-10541323.3536*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-1827904*(7796.8368+5400.40*cos(Y[1]))^2-730134.08*(7796.8368+5400.40*cos(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])-730134.08*sin(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-394301608.5632*sin(Y[1]+Y[3])^2*(142796.8368+10800.80*cos(Y[1]))); YP[6] := (540.04*cos(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))-730134.08*cos(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))+291643.2016*cos(Y[1]+Y[3])*sin(Y[1]+Y[3])*(142796.8368+10800.80*cos(Y[1]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))-291643.2016*cos(Y[1]+Y[3])*sin(Y[1]+Y[3])*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+730134.08*cos(Y[1]+Y[3])*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(142796.8368+10800.80*cos(Y[1]))-540.04*cos(Y[1]+Y[3])*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-7796.8368*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))+10541323.3536*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))-540.04*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*sin(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))-291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*sin(Y[1]+Y[3])^2*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))-1352*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(7796.8368+5400.40*cos(Y[1]))-540.04*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])-10541323.3536*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*(142796.8368+10800.80*cos(Y[1]))+7796.8368*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+1352*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*(7796.8368+5400.40*cos(Y[1]))^2+540.04*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*(7796.8368+5400.40*cos(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])+540.04*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*sin(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+291643.2016*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*sin(Y[1]+Y[3])^2*(142796.8368+10800.80*cos(Y[1])))/(1460268.16*cos(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))-394301608.5632*cos(Y[1]+Y[3])^2*(142796.8368+10800.80*cos(Y[1]))+291643.2016*cos(Y[1]+Y[3])^2*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+291643.2016*cos(Y[1]+Y[3])*sin(Y[1]+Y[3])*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-10541323.3536*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2+291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*cos(Y[1]+Y[3])*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])+291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2*sin(Y[1]+Y[3])^2+2035121836544224.7506+153931588575265.01376*cos(Y[1])-10541323.3536*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-1827904*(7796.8368+5400.40*cos(Y[1]))^2-730134.08*(7796.8368+5400.40*cos(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])-730134.08*sin(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-394301608.5632*sin(Y[1]+Y[3])^2*(142796.8368+10800.80*cos(Y[1]))); YP[8] := -(291643.2016*cos(Y[1]+Y[3])^2*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-540.04*cos(Y[1]+Y[3])*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+1080.08*cos(Y[1]+Y[3])*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))*(7796.8368+5400.40*cos(Y[1]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))-291643.2016*cos(Y[1]+Y[3])^2*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))*(142796.8368+10800.80*cos(Y[1]))-730134.08*sin(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))+730134.08*sin(Y[1]+Y[3])*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(142796.8368+10800.80*cos(Y[1]))-7796.8368*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2+10541323.3536*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))*(142796.8368+10800.80*cos(Y[1]))-1352*(5870*Y[4]^2*cos(Y[3])+540.04*(Y[4]+Y[2])^2*cos(Y[1]+Y[3])+13263.12+4502790.000*Y[7]+8441411.753*cosh(0.6003043287e-1+0.2001014429e-1*Y[7])*(cos(.43*X-.3001521644)-cos(.43*X+.3001521644)))*(7796.8368+5400.40*cos(Y[1]))^2+540.04*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*sin(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))-291643.2016*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*sin(Y[1]+Y[3])*cos(Y[1]+Y[3])*(142796.8368+10800.80*cos(Y[1]))+291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*cos(Y[1]+Y[3])*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))*sin(Y[1]+Y[3])-540.04*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*sin(Y[1]+Y[3])-10541323.3536*(-587*sin(Y[1])*(9.20*Y[2]^2-9.20*(Y[4]+Y[2])^2)+5297.7924*sin(Y[1]+Y[3])+57584.70*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+1352*(-5297.7924*sin(Y[1]+Y[3])+5400.40*Y[4]^2*sin(Y[1]))*(7796.8368+5400.40*cos(Y[1]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+7796.8368*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-540.04*(5870*Y[4]^2*sin(Y[3])+540.04*(Y[4]+Y[2])^2*sin(Y[1]+Y[3])+2710.493534*sin(.43*X-0.2001014429e-1*Y[5]))*cos(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3])))/(1460268.16*cos(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))-394301608.5632*cos(Y[1]+Y[3])^2*(142796.8368+10800.80*cos(Y[1]))+291643.2016*cos(Y[1]+Y[3])^2*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))+291643.2016*cos(Y[1]+Y[3])*sin(Y[1]+Y[3])*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-10541323.3536*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2+291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))*cos(Y[1]+Y[3])*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])+291643.2016*(5870*cos(Y[3])+540.04*cos(Y[1]+Y[3]))^2*sin(Y[1]+Y[3])^2+2035121836544224.7506+153931588575265.01376*cos(Y[1])-10541323.3536*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-1827904*(7796.8368+5400.40*cos(Y[1]))^2-730134.08*(7796.8368+5400.40*cos(Y[1]))*(-540.04*sin(Y[1]+Y[3])-5870*sin(Y[3]))*sin(Y[1]+Y[3])-730134.08*sin(Y[1]+Y[3])*(7796.8368+5400.40*cos(Y[1]))*(-5870*sin(Y[1]+Y[3])-5870*sin(Y[3]))-394301608.5632*sin(Y[1]+Y[3])^2*(142796.8368+10800.80*cos(Y[1]))); YP[1] := Y[2]; YP[3] := Y[4]; YP[5] := Y[6]; YP[7] := Y[8]; 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 18 ) = ([]), ( 19 ) = (0)  ] ))  ] ); _y0 := Array(0..8, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0., (7) = 0., (8) = 0.}); _vmap := array( 1 .. 8, [( 1 ) = (1), ( 2 ) = (2), ( 3 ) = (3), ( 5 ) = (5), ( 4 ) = (4), ( 7 ) = (7), ( 6 ) = (6), ( 8 ) = (8)  ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); if _par <> [] then `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) end if; `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 10 and 10 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 10 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 10 and 10 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 10 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-10 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-10; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch:  end try else try procname(procname("right")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch:  end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 10 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error  end try; if _src = 0 and 10 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif 10 < _dat[4][9] then if _dat[4][9]-10 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-10, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif 10 < _dat[4][9] then if _dat[4][9]-10 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-10, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; _dat[4][26] := _EnvDSNumericSaveDigits; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(0..0, {}), (3) = [t, alpha(t), diff(alpha(t), t), theta(t), diff(theta(t), t), x(t), diff(x(t), t), z(t), diff(z(t), t)], (4) = []}); _vars := _dat[3]; _pars := map(rhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_rkf45, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_rkf45, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_rkf45, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_rkf45, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_rkf45), 'string') = rhs(x_rkf45); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_rkf45), 'string') = rhs(x_rkf45)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_rkf45) else _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_rkf45) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error  end try end proc

(10)

``

odeplot(solution,[[t,x(t)],[t,alpha(t)],[t,z(t)],[t,theta(t)]], t=0..1000, thickness=2);

Warning, cannot evaluate the solution further right of 46.041076, maxfun limit exceeded (see ?dsolve,maxfun for details)

 

 

 

odeplot(solution,[[t,x(t)]], t=0..1000, thickness=2);

Warning, cannot evaluate the solution further right of 46.041076, maxfun limit exceeded (see ?dsolve,maxfun for details)

 

 

 

odeplot(solution,[[t,z(t)]], t=0..1000, thickness=2);

Warning, cannot evaluate the solution further right of 46.041076, maxfun limit exceeded (see ?dsolve,maxfun for details)

 

 

 

odeplot(solution,[[t,alpha(t)]], t=0..1000, thickness=2);

Warning, cannot evaluate the solution further right of 46.041076, maxfun limit exceeded (see ?dsolve,maxfun for details)

 

 

 

odeplot(solution,[[t,theta(t)]], t=0..1000, thickness=2);

Warning, cannot evaluate the solution further right of 46.041076, maxfun limit exceeded (see ?dsolve,maxfun for details)

 

 

thank you 

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