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Question: Poincare section

Question:Poincare section

GambiaMan 15 Maple
ode
December 04 2015
0

Hello,

I have a question about poincare sections. I have this piece of code i need to analyse and I want to use a poincare section in order to so. How could I do it? I am interested in theta and omega. Any help is greatly appreciated! Thank you in advance!

Kind regards,

Gambia Man

> 

with(plots):
> 

a := 1.501*10^9:
> 

Th := sqrt(4*Pi^2*a^3/(G*(Mh+Msat)));

1876321.326

  

0.3348672330e-5

 (1)
> 

HyperionOrbit := proc (`θIC`, `ωIC`) local a, Mh, Msat, G, e, beta, M, Eqns, ICs; global `ωH`, Th, soln; a := 1.501*10^9; Mh := 5.5855*10^18; Msat := 5.6832*10^26; G := 6.67259/10^11; e := .232; beta := .89; M := Mh+Msat; Eqns := diff(theta(t), t) = omega(t), diff(omega(t), t) = -G*Msat*beta^2*(xH(t)*sin(theta(t))-yH(t)*cos(theta(t)))*(xH(t)*cos(theta(t))+yH(t)*sin(theta(t)))/(xH(t)^2+yH(t)^2)^2.5, diff(xH(t), t) = vxH(t), diff(vxH(t), t) = -G*M*xH(t)/(xH(t)^2+yH(t)^2)^(3/2), diff(yH(t), t) = vyH(t), diff(vyH(t), t) = -G*M*yH(t)/(xH(t)^2+yH(t)^2)^(3/2); ICs := xH(0) = a*(1+e), yH(0) = 0, vxH(0) = 0, vyH(0) = sqrt(G*M*(1-e)/(a*(1+e))), theta(0) = `θIC`, omega(0) = `ωIC`; soln := dsolve({Eqns, ICs}, numeric); odeplot(soln, [theta(t), omega(t)/`ωH`], 0 .. 5*Th, numpoints = 2000, labels = ["θ(t)","ω(t)/ωH"], axes = boxed, size = [.25, .75]) end proc
> 

``

 

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