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These are replies submitted by GambiaMan

Just to add, the result is meant to look like this. Thanks again!

I dont think the picture uploaded in the original message. Here it is again.

@ThU Thank you for the help!

@Preben Alsholm It works! Thanks a lot!!

@Preben Alsholm Thank you so much mate! Seriously you solved a problem I was trying for the last 4 hours!

@Preben Alsholm Thank you so much for the help!

@Markiyan Hirnyk Nevermind I managed to get it to work!!! Thanks for the help!!!

@Markiyan Hirnyk Thank you for your reply! I tried to input what you have suggested unfortunately an error comes up. 


a := 1.501*10^9:

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

HyperionOrbit := proc (`θIC`, `ωIC`, n, nopoints) local a, Mh, Msat, G, e, beta, M, Eqns, ICs, soln; global `ωH`, Th; 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, maxfun = 0, output = array([seq(i, i = 0 .. nTh, Th)])); plots:-odeplot(soln, [theta(t), omega(t)/`ωH`], 0 .. n*Th, numpoints = nopoints, labels = ["θ(t)","ω(t)/ωH"], axes = boxed) end proc:

HyperionOrbit(.5, 1.8*`ωH`, 5, 10000)

Error, (in HyperionOrbit) unable to execute seq





@Preben Alsholm To be honest I'm not sure what the plot looks like, all I know is that it undergoes chaotic behaviour. What I need to extract are the values for theta and omega at integer values of Th and then plot just those values. That is why I tried to use the sample option. The number of points is there for the plot between two intervals.

@Preben Alsholm Hello,

Thank you your reply. Is there any alternative to doing this?


@Carl Love Thanks a lot for the advice!!!

@Preben Alsholm This has helped me a lot thank you so much!

@Kitonum Thank you so much for the help!

@Thomas Richard Thank you very much :) my problem has been resolved.



Thank you so much for your reply I understand all the stupid mistakes ive made. I'll be more careful next time, again thank you for taking your time in replying to this question. 

Kind regards, 

Gambia Man

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