ODE solver for restricted 3 body problem

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I am trying to implement the following problem(restricted 3 body problem), but I don't know if my implementation is correct since the plot does not look right to me (niether phase plane nor in time). Is my impementation correct? I converted the 2nd order ODE system of 1st order and used the given parameters. Here is the problem and my code
clc,clear,close all
mu = 0.012277471
Y0 = [0.994; 0.0; 0.0; -2.00158510637908252240527862224];
t0 = 0;
T = 17.0652164601579625588917206249;
tspan = [t0 T];
options = odeset('RelTol',1e-13,'AbsTol',1e-16 * ones(4,1));
[t,Y] = ode15s(@(t,Y) ThreeBodyProblem(t,Y,mu), tspan, Y0,options);
Y = Y';
plot(t,Y)
% plot(Y(2,:),Y(4,:))
function dydt = ThreeBodyProblem(t,y,mu)
dydt = zeros(4,1);
mu_p = 1 - mu;
D1 = ( (y(1) + mu)^2 + y(3)^2 )^(3/2);
D2 = ( (y(1) - mu_p)^2 + y(3)^2 )^(3/2);
dydt(1) = y(2);
dydt(2) = y(1) + 2 * dydt(3) - mu_p * ((y(1) + mu)/D1) - mu * ((y(1) - mu)/D2);
dydt(3) = y(4);
dydt(4) = y(3) + 2 * dydt(1) - mu_p * (y(3)/D1) - mu * (y(3)/D2);
end

Accepted Answer

James Tursa
James Tursa on 19 Sep 2022
Edited: James Tursa on 19 Sep 2022
In this line:
dydt(2) = y(1) + 2 * dydt(3) - mu_p * ((y(1) + mu)/D1) - mu * ((y(1) - mu)/D2);
you use dydt(3) before you set its value, so this is incorrect. Simply reorder your equations to avoid this (or use y(4) instead of dydt(3) on rhs). Also it looks like you have some typos with signs and mu prime stuff. E.g.,
dydt(1) = y(2);
dydt(3) = y(4);
dydt(2) = y(1) + 2 * dydt(3) - mu_p * ((y(1) + mu)/D1) - mu * ((y(1) - mu_p)/D2);
dydt(4) = y(3) - 2 * dydt(1) - mu_p * (y(3)/D1) - mu * (y(3)/D2);
Side note: You have 30 digits of precision listed for a couple of your values, but double precision only has about 15 digits of precision, so those trailing digits are meaningless.
  2 Comments
James Tursa
James Tursa on 19 Sep 2022
Edited: James Tursa on 19 Sep 2022
You would have to set everything up as an extended precision problem, e.g. using the Symbolic Toolbox or similar, and also write your own numeric solver instead of using ode15s( ). Probably not worth it. Do you really know those values to that precision anyway? Where do they come from?

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R2021b

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