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I have been having problems with using the BodePlot function with units:

 

R1 := 18.2*10^3*Unit('Omega');

R2 := 10^3*Unit('Omega');

C1 := 470*10^(-12)*Unit('F');

C2 := 4.7*10^(-9)*Unit('F');

# wo is in hertz

wo := 1/sqrt(R1*R2*C1*C2);

# Q is unitless

Q := wo*R1*R2*C2/(R1+R2)

 

with(DynamicSystems);

sys := TransferFunction(wo^2/(s^2+wo*s/Q+wo^2));

 

This is the error message I got:

Error, (in Units:-Standard:-+) the units `1` and `Hz` have incompatible dimensions

 

I think the problem is that the BodePlot function doesn't expect 'wo' to have units.  

So I tried to work around the issue by using the loglogplot but it doesn't seem to like 

complex function even when I used abs to find the magnitude (with or without units).

 

 Any workaround is appreciated.

I'm trying to resolve a differential equation system and plot it. But when I use the "odeplot" command, just appear the words in blue and there's no graphic. Does anyone know whats happening?

 

This is a typical problem of what I find when learning DynamicSystems. Basically, I create number of systems by changing one paramter (the damping ratio in this case) and want to plot the unit step of all of them on the same plot to compare the effect of the damping ratio.

I setup the TransferFunction, used Simulate to obtain the response of each to the same input. The problem comes when I want to plot the respones.  I have to use plot[odeplot] it seems. But this only like to take one response at a time.

I can't use plot() since I do not have the actual function of the response in time. Unless I try to extract the differential equation from the sytem object, solve that and get a solution then use plot(). But if I do all of this, what do I need DynamicSystems in first place? 

I will show what I tried. I am sure there is some way to do this in Maple I just do not know yet the correct function or setup.

restart;
alias(DS=DynamicSystems);
H:=(w,zeta)->w^2/(s^2+2*zeta*w*s+w^2);
sys:= (w,zeta)->DS:-TransferFunction(H(w,zeta)):
sol:=seq(DS:-Simulate(sys(1,zeta),Heaviside(t)),zeta=0.1..1.2,.2):

Now I want to plot all the solutions in sol. I wanted to use plot(...) only to be able to obtain the automatic coloring of each solution.

If I try to use plots[odeplot], it works, but only on one at a time:

plots[odeplot](sol[1],t=0..10);

If I try this, it fails:

plots[odeplot]([sol],t=0..10);

I can get each plot separatly and then use display() but then lose the automatic coloring of the lines:

plots:-display(seq(plots[odeplot](sol[i],t=0..10),i=1..nops([sol])));

I am looking for the above plot, but have the lines each colors differently. I also need to figure how to add legend later. But one step at a time. I can't hard code the color in the plots[odeplot] call itself, since I do not know what color to give each line. plot([....],t=0..) allready does this automatically. But I can't use it!

Just to give an idea of the kind of plot I am trying to obtain, here it is in Mathematica:

sys = TransferFunctionModel[w^2/(s^2 + 2 z*w*s + w^2), s];
zValues = Range[.2, 1.2, .2];
fun = OutputResponse[sys /. {w -> 1, z -> #}, UnitStep[t], {t, 0, 12}] & /@ zValues;
Plot[Evaluate@Flatten@Table[fun[[i]], {i, 1, Length[fun]}], {t, 0, 12}, Frame -> True, PlotRange -> {{0, 12}, {-.1, 1.7}}]

 

 

 

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

Hi, 

I want to animate this code 

plots[odeplot](Trajectoire, [[x1(t), y1(t), t], [x2(t), y2(t), t], [x3(t), y3(t), t], [x4(t), y4(t), t], [x5(t), y5(t), t], [x6(t), y6(t), t], [x7(t), y7(t),t], [x8(t), y8(t), t], [x9(t), y9(t), t], [xA(t), yA(t), t]], TempsInitial..TempsFinal, numpoints = 10000,axes=boxed, scaling = constrained);

However, Maple 16 is giving me an error message :

Error, (in plots/animate) the first argument must be a procedure


I don't know how I can do to animate this code.

 

Thanks!

I encounter "insufficient  initial/boundary value" error message,  do know how to proceed from there, search with "insufficient initial value" gets no result. Any help will be appreciated.

 

 

> restart; alias(r = r(t), f = f(t)); with(plots);
r, f
> DE := diff(r, t) = 2*r+alpha*r*f, diff(f, t) = -f+alpha*r*f;
d d
--- r = 2 r + alpha r f, --- f = -f + alpha r f
dt dt
> NULL;
> params := alpha = .3;
alpha = 0.3
> initv := r(0) = 101, f(0) = 2;
> NULL;
>
> dvars := [r, t];
> chaodisplay := proc (chartname) EQ := [op(subs(params, [DE])), initv]; EQ1 := dsolve(EQ, numeric); odeplot(EQ1, dvars, t = 0 .. 300, axes = frame, numpoints = 50000, color = green, orientation = [-30, 100], title = chartname) end proc;
Warning, `EQ` is implicitly declared local to procedure `chaodisplay`
Warning, `EQ1` is implicitly declared local to procedure `chaodisplay`
>
> chaodisplay("Rabbit and Fox");
Error, (in dsolve/numeric/type_check) insufficient initial/boundary value information for procedure defined problem
>

Hello,

I am solving eq1 and then plot it using odeplot. Then I am extracting data from odeplot using op[1,1]. From that I only care about  one point so I am using pt[1] := dt[1]([1, 2]); then I ploted it using pointplot. I run a do loop and at the end I am ploting all the points.

My code works fine but I am trying to have a line contacting each points. I tried  style=line but it did not work.

How can I have a line contacting each points on my final plot (which is display([pl[1], seq(allpl[k], k = 1 .. 3)])) ?

This is my code:

> restart; with(DEtools); with(plots);
> with(DEtools); with(plots);
> A := 0.2e-1; B := 10^(-5); k := 0;
> eq1 := diff(X(t), t) = -(A+B*X(t))*X(t);

> ic[1] := X(365*k) = 1000;
> s[1] := dsolve({eq1, ic[1]}, X(t), range = 0 .. .365, numeric);
> p[1] := odeplot(s[1], [[t, X(t)]], t = 0 .. .365);
> dt[1] := op([1, 1], p[1]);
> pt[1] := dt[1]([1, 2]);
> pl[1] := pointplot(pt[1], axes = boxed);
> for k to 3 do
tk := 365*k;
A := rhs(s[k](tk)[2]);
ic[k+1] := X(tk) = 500.*A;
s[k+1] := dsolve({eq1, ic[k+1]}, X(t), range = tk .. 2*tk, numeric);
p[k+1] := odeplot(s[k+1], [[t, X(t)]], t = tk .. 2*tk);
dt[k+1] := op([1, 1], p[k+1]);
pt[k+1] := dt[k+1]([1, 2]);
pl[k+1] := pointplot(pt[k+1], axes = boxed);
allpl[k] := display([pl[k+1]])
end do;
> display([pl[1], seq(allpl[k], k = 1 .. 3)]);

 

Thank you

Hi

I'm trying to make a phase portrait for coupled oscillators. No problem for the following lines

Hello,

After we solved two equations we want to plot them with two sliders. I am trying to have two sliders for k and mu. I followed what this link suggested:

http://www.mapleprimes.com/questions/119732-How-To-Code-Sliders-To-Make-It-Easy

But I get this warning:

Warning, `p1` is implicitly declared local to procedure `myplot`
 

Hi,

 

I have two differential equations describing a solar sail in 2D.

One is my radial direction and one is the tangential direction.

I have plotted r(t) and theta(t) but I want r(theta) so I have assigned my two differential equations and initial conditions, have my two plots for r and theta in terms of t and then I have used the following command to plot in polar coordinates:

 

 

I have already solved my ODEs and used odeplot to analyse the change over time (0 to 10).

Below is my ODE,

d(a(t))/dt = x - y*(a(t))

d(b(t))/dt = m*a - n*(b(t))

 

My query here is,

I need to substitute a(t) and b(t) in a seperate equation,

h(t) = 60/0.98 * (a(t))*(b(t))

and i need to plot 'h' over time (0 to 10)

How do I go about doing this?

Please help.

Thanks.

Hi everyone i've tried to solve two coupled nonlinear ode but maple gives me these two errors can you help me with this?

 

ode1 := diff(f(x), x, x, x)+3*f(x)*(diff(f(x), x, x))-2*(diff(f(x), x))^2+g(x) = 0;
 ode2 := diff(g(x), x, x)+(3*10)*f(x)*(diff(g(x), x)) = 0;
 bcs1 := (D(f))(0) = 0, f(0) = 0, (D(f))(6) = 0;
 bcs2 := g(0) = 1, g(6) = 0;
 sys := {bcs1, bcs2, ode1, ode2};
 dsn := dsolve(sys, numeric);
 print(plots:-odeplot(dsn, [x, g(x)...

Hi,

Assume having to solve an ode with dsolve and plotting with odeplot. Further, markings at specific parameter values of the solution should be plotted, i.e. if p is the solution of the ode, the points p(t1), p(t2), ... should be plotted. Since the ode is complicated and computation takes a lot of time, is there a way to extract the values p(t1), ... from the odeplot result directly without invoking calls like subs(p(0.5),b(s)) again?

Hello everyone. I'm a french student and I make a study on the double pendulum. I have written all of the equations into maple (6 equation for solid movement and 2 for point movement). We will work with 2 equations.

So i got my 2 differential equations (non linear) and I want to odeplot them and after plot the 2 solutions with plot.

Unfortunatly, after reading some post here and solutions, my problem still exist. When I odeplot my solutions : i have a warning message (so also when I plot) :

I want to solve the position of a bal with a variable angel of the start velocity. I want to know which angle I have to take when the ball must be in a fully known position (5.44 , 1.60).I must also take the friction into account.

Therefore I have a system of equitations that I can solve with dsolve if I fill in the angle (in degrees).

> dsolve(eval(stlsl,angle = angeltest), numeric);

It gives me back values in x(t) and y(t). But know I want to make...

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