MaplePrimes Questions

Hello, 

    I'm finding Maple very useful. I'm a student but not very far along, only in MATH-1075 (intermediate algebra).

 

I have learned how to plot equations using the context menu, and the smartplot() command.

 

I have two questions I have not been able to discover an answer for.

 

When I plot an equation, how can I ask Maple to tell me coordinates of X & Y intercepts?

When I plot 2 equations, how can I ask Maple to tell me coodinates of intersections?

 

thanks in advance for any help. I tried to look up myself how to do this but was unsuccessful :(

 

Brent

Hi every body:

i will plot this function in maple in domain x=0..1,but when use the plot commond i see this warning:

Warning, unable to evaluate the function to numeric values in the region; complex values were detected

how can I plot it?

eq := 4.728139762*10^(-14)*sqrt((-5.905404581*10^83*x^4-1.382542004*10^88*x^2+2.271592177*10^92+1.631888578*10^79*x^6+2.795756904*10^23*sqrt(-1.317535223*10^121*x^8+6.370084310*10^125*x^6-7.852926774*10^129*x^4+2.223707894*10^132*x^2-1.592721566*10^134))^(1/3)*(-(1.114348319*10^53*I)*x^4-6.433693022*10^52*x^4+(2.688368867*10^57*I)*x^2+1.552130489*10^57*x^2+5.072945110*10^26*x^2*(-5.905404581*10^83*x^4-1.382542004*10^88*x^2+2.271592177*10^92+1.631888578*10^79*x^6+2.795756904*10^23*sqrt(-1.317535223*10^121*x^8+6.370084310*10^125*x^6-7.852926774*10^129*x^4+2.223707894*10^132*x^2-1.592721566*10^134))^(1/3)-3.723246850*10^61-6.448852713*10^61*I+(1.732050808*I)*(-5.905404581*10^83*x^4-1.382542004*10^88*x^2+2.271592177*10^92+1.631888578*10^79*x^6+2.795756904*10^23*sqrt(-1.317535223*10^121*x^8+6.370084310*10^125*x^6-7.852926774*10^129*x^4+2.223707894*10^132*x^2-1.592721566*10^134))^(2/3)+1.231339558*10^31*(-5.905404581*10^83*x^4-1.382542004*10^88*x^2+2.271592177*10^92+1.631888578*10^79*x^6+2.795756904*10^23*sqrt(-1.317535223*10^121*x^8+6.370084310*10^125*x^6-7.852926774*10^129*x^4+2.223707894*10^132*x^2-1.592721566*10^134))^(1/3)-1.*(-5.905404581*10^83*x^4-1.382542004*10^88*x^2+2.271592177*10^92+1.631888578*10^79*x^6+2.795756904*10^23*sqrt(-1.317535223*10^121*x^8+6.370084310*10^125*x^6-7.852926774*10^129*x^4+2.223707894*10^132*x^2-1.592721566*10^134))^(2/3)))/(-5.905404581*10^83*x^4-1.382542004*10^88*x^2+2.271592177*10^92+1.631888578*10^79*x^6+2.795756904*10^23*sqrt(-1.317535223*10^121*x^8+6.370084310*10^125*x^6-7.852926774*10^129*x^4+2.223707894*10^132*x^2-1.592721566*10^134))^(1/3)

with regards...

 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 

sign is different runnning the same script in maple 12 and maple 15 in different machine, just using matrixmultiply and matrix(xxx, shape=hermitian)

assume my window 7 infected by virus, can maple prevent virus change

its accuracy?

or

is there any change between maple 12 and maple 15? 

 

i feel that i will have to make large effort in order to find reason such as reinstall maple 12.

 

window 7 maple 15

[[a = 3.720799777 10 , b = -3.720817167 10 ]], 0.3469023622
[(-0.737729376724384 + 0. I) ((-0.737729376724384100 + 0. I) a

+ (-0.738311510115612690 + 0. I) b) + (-0.590656319609631

- 0. I) ((-0.590656319609630831 + 0. I) a

+ (-0.589459378339369122 + 0. I) b) + (0.326925800179577

- 0. I) ((0.326925800179577230 + 0. I) a

+ (0.327770888454982090 + 0. I) b) = -0.736196608749071 + 0. I,

(-0.590656319609631 + 0. I) ((-0.591008582207233624 + 0. I) a

+ (-0.589459378339369010 + 0. I) b) + (0.331003458223746

+ 0. I) ((0.331003458223746439 + 0. I) a

+ (0.327770888454981812 + 0. I) b) + (-0.735625969091165

- 0. I) ((-0.735625969091165288 + 0. I) a

+ (-0.738311510115613134 + 0. I) b) = 0.327869065042947 + 0. I

]

window 8 maple 12

 


[[a = 0.2249293777, b = 1.221244758]], 0.9888653482, "************"
[(0.737729376724384100 + 0. I) ((0.737729376724384100 + 0. I) a

+ (-0.738311510115612690 + 0. I) b) + (0.590656319609631053 - 0. I)

((0.590656319609631053 + 0. I) a + (-0.589459378339369122 + 0. I) b) +

(0.326925800179576676 - 0. I) ((0.326925800179576676 + 0. I) a

+ (0.327770888454982090 + 0. I) b) = -0.736196608749071002 + 0. I,

(0.590656319609631053 + 0. I) ((0.591008582207233624 + 0. I) a

+ (-0.589459378339369010 + 0. I) b) + (-0.331003458223746605 + 0. I) ((
-0.331003458223746605 + 0. I) a + (0.327770888454981812 + 0. I) b) + (
-0.735625969091165178 - 0. I) ((-0.735625969091165178 + 0. I) a

+ (-0.738311510115613134 + 0. I) b) = 0.327869065042946218 + 0. I]
7

 

please help me to find an analytical approach to the below equation:

> ode3 := diff(n(t), t)+(1/2)*(-(3.707186000*(0.815e-1*(diff(n(t), t, t))+diff(n(t), t)))/(0.815e-1*(diff(n(t), t))+n(t))^(3/2)-(.1428*(1+0.714e-1*n(t)))*(diff(n(t), t)))/sqrt(7.414372/sqrt(0.815e-1*(diff(n(t), t))+n(t))-(1+0.714e-1*n(t))^2)+n(t)+sqrt(7.414372/sqrt(0.815e-1*(diff(n(t), t))+n(t))-(1+0.714e-1*n(t))^2)-(2.518891688*(1+.3570*n(t)))*sqrt(0.815e-1*(diff(n(t), t))+n(t)) = 0;
                                                                           /
                                                                           |
/ d      \                                 1                               |
|--- n(t)| + ------------------------------------------------------------- |
\ dt     /                                                           (1/2) |
               /           7.414372                                2\      |
             2 |------------------------------- - (1 + 0.0714 n(t)) |      |
               |                          (1/2)                     |      \
               |/       / d      \       \                          |       
               ||0.0815 |--- n(t)| + n(t)|                          |       
               \\       \ dt     /       /                          /       
              /       / d  / d      \\   / d      \\
  3.707186000 |0.0815 |--- |--- n(t)|| + |--- n(t)||
              \       \ dt \ dt     //   \ dt     //
- --------------------------------------------------
                                     (3/2)          
           /       / d      \       \               
           |0.0815 |--- n(t)| + n(t)|               
           \       \ dt     /       /               

                                        \       
                                        |       
                              / d      \|       
   - 0.1428 (1 + 0.0714 n(t)) |--- n(t)|| + n(t)
                              \ dt     /|       
                                        |       
                                        |       
                                        /       

                                                           (1/2)
     /           7.414372                                2\     
   + |------------------------------- - (1 + 0.0714 n(t)) |     
     |                          (1/2)                     |     
     |/       / d      \       \                          |     
     ||0.0815 |--- n(t)| + n(t)|                          |     
     \\       \ dt     /       /                          /     

                                                             (1/2)    
                                   /       / d      \       \         
   - 2.518891688 (1 + 0.3570 n(t)) |0.0815 |--- n(t)| + n(t)|      = 0
                                   \       \ dt     /       /         
> ics := n(0) = 0, (D(n))(0) = 674.5142595;


thanks and regards

louiza

 

How to create animation f(x)=x^2, g(x)=sqrt(x), x=0, and x=1 if rotation about line y=-1 and x=-1?

Thank for your attention and helping.

Hello everybody,

I am trying to solve a partial differential equation (wave equation) with initial conditions that contain derivative and x-varying values

My equation
Uxx – Utt = 0 (hiperbólica) where xx and tt denote second partial derivatives with respect to x and t
0 <= x <= 10; t > 0;
u(0,t) = u(10,t) = 0;
Ut(x,0) = 0;
u(x,0)=
x for 0 <= x < 5
10-x for 5 <= x <= 10

I ve defined my equation as follow
> PDE := diff(u(x,t),x,x)=diff(u(x,t),t,t);

I m first trying without the x-varying initial condition.

> IBC := {u(0,t)=0,u(10,t)=0,u(x,0)=10-x,diff(u(x,0), t) = 0};
Returns the ugly

And that gives error when trying to solve
> pds := pdsolve(PDE,IBC,numeric);
Error, (in pdsolve/numeric/process_IBCs) initial/boundary condition does not contain the dependent variables of the PDE: 0 = 0

Another try with
> IBC := {u(0,t)=0,u(10,t)=0,u(x,0)=10-x,diff(u(x,t=0), t) = 0};

Looks like more promissing but returns (in a solving attempt)
> pds := pdsolve(PDE,IBC,numeric);

Error, (in pdsolve/numeric/process_IBCs) initial/boundary conditions must depend upon exactly one of the independent variables: diff(u(x, t = 0), t) = 0


Regarding the x varying initial condition, I ve tried the `assuming` keyword in various attempts but without success.

Anybody could help on the matter?


Thanks in advance for anytip.
Have a good day
Nicolas

Hello those in Mapleprimes,

I want to obtain the result of the following codes,

shift:=(f::procedure)->(x->(f(x+1))):

shift(sin);

 

as x->sin(x+1)..................(1)

 

But, the result I could get was only

x -> f(x + 1)......................(2)

 

Please teach me how I can obtain the result as (1), not (2)?

 

Thanks in advance.

 

taro

Hello,

I have a easy question I think but blocking for me.

I have a expression g(t):=f(x(t),alpha(t),beta(t))

I give 

x(t):=0.12
alpha(t):=0
beta(t):=0

I would like to evaluate g(t).

And for the moment x(t), alpha(t) and beta(t) aren't replaced by their values.

How can i do in order to have the evaluation of g(t) ?

Thanks a lot for help.

 

i am using plot command to plot the first vs the second column in the attached file A.txt

it is giving a strange plot. while plotting the first vs second column in kgraph i am getting the correct plot

why is maple giving me a wrong plot 

you can find the two plots and the raw data file A.txt

Download A.txt

 

Dihedralgroup(9) acts on the set 1..9 and has order 9

g:=SmallGroup(18,1) acts on the set 1..18 and has order 18.

Question:

Is it possible to let g act on 1..9, too) and how can I do that?

Best regards

 

Kurt Ewald

Hallo,

Is there a fairly straightforward method for obtaining an array of coordinates from an implicit equation? I have an ellipse defined implicitly (by a horrendously involved expression) and can't figure out how to extract a set of coordinates from an implicitplot. I'm reluctant to use seq and fsolve with a fixed stepsize.

Would be grateful for some insight!

Thanks.

Weirp

Hi Mapleprimers,

I was wondering if there way a way to use restart(); and clear Maple's memory, but protect the memory in a certain variable?  I would like to return the memory to the operating system, but keep a symholic function in memory.

Alternatively, is there a way to save a symbolic function to a file, then reload it at a seperate time?

 

hi everyone,i have two questions,
1. i have a problem with select command? 

restart:

eq[1]:=diff(a[1](x),x$2)+diff(a[1](x),x$1)*diff(a[2](x),x$1)+diff(a[1](x),x$2)*diff(a[2](x),x$2)+diff(a[3](x),x$1)+diff(a[1](x),x$1)*diff(a[2](x),x$2)+diff(a[1](x),x$2)*diff(a[3](x),x$1);

diff(diff(a[1](x), x), x)+(diff(a[1](x), x))*(diff(a[2](x), x))+(diff(diff(a[1](x), x), x))*(diff(diff(a[2](x), x), x))+diff(a[3](x), x)+(diff(a[1](x), x))*(diff(diff(a[2](x), x), x))+(diff(diff(a[1](x), x), x))*(diff(a[3](x), x))

(1)

# how can i select the differentials which are of second order ? without using the function names , for example i do not want to use this :

select(has,eq[1],[seq](diff(a[i](x),x$2),i=1..3));

diff(diff(a[1](x), x), x)+(diff(diff(a[1](x), x), x))*(diff(diff(a[2](x), x), x))+(diff(a[1](x), x))*(diff(diff(a[2](x), x), x))+(diff(diff(a[1](x), x), x))*(diff(a[3](x), x))

(2)

#i just want maple to select the second order differentials,without knowing its name # just beacuse it is of second order,how can i do this !?

2. how i can select the parts which their addition of differential oreder,are the same ? for example,the second expression in eq[1] has the addition order of 2,third has 4 and ... how can isolate addition order ? tnx in advance . 

Download select.mw

Hi All. Hope all is well.

Assume that we have partitioned [0,a], into N equidistant subintervals and in each subinterval we have M sets of polynomials of arbitrary form[say bij(t)](a.e Taylor series, or Bernstein series,…)

for Example with N=4, M=3 and by Taylor series we have:

 

now we want to approximate a function, asy f(t), in this interval with following form:

 

If we have:

(Tau is a constant number)
then: How can  we find L and Z matrices using maple? Is it any way? (or other softwares?)

Regards

 

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

 

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