MATLAB: Solving a system of 4 second order differential equations

Question

Best Answer

I believe that re and rm should be functions too

re = @(z) sqrt((z(1)+E)^2+z(3)^2);
rm = @(z) sqrt((z(1)-M)^2+z(3)^2);
zprime = @(t,z) [z(2)
    2*z(4)+z(1)-((M*(z(1)+E))/re(z)^3)-((E*(z(1)-M))/rm(z)^3)
    z(4)
    -2*z(2)+z(3)-((M*z(3))/re(z)^3)-((E*z(3))/rm(z)^3)];
tspan = [0 5e-3];
z0 = [0 1 0 1];
[t, z] = ode45(zprime,tspan,z0);

Pay attention

Related Solutions

MATLAB: Solving odes (resiscted 3 body problem)

Building matrices with [ ] can be picky when it comes to spaces. E.g.,

>> [1;5-3;4]
ans =
     1
     2
     4
>> [1;5 -3;4]
??? Error using ==> vertcat
CAT arguments dimensions are not consistent.
>> [1;(5 -3);4]
ans =
     1
     2
     4

In the second case above, because of that extra space the parser interpreted the "5 -3" as a 1x2 vector and not as a single scalar. To fix this, either get rid of all of your spaces, or use parentheses as shown.

Side Note: Your line 10 seems to be missing some E's and M's when compared to your posted equations. You might check that.

MATLAB: Solving odes (restricted 3 body problems)

Variables rE and rM should be in the function

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Answer 1

I believe that re and rm should be functions too

re = @(z) sqrt((z(1)+E)^2+z(3)^2);
rm = @(z) sqrt((z(1)-M)^2+z(3)^2);
zprime = @(t,z) [z(2)
    2*z(4)+z(1)-((M*(z(1)+E))/re(z)^3)-((E*(z(1)-M))/rm(z)^3)
    z(4)
    -2*z(2)+z(3)-((M*z(3))/re(z)^3)-((E*z(3))/rm(z)^3)];
tspan = [0 5e-3];
z0 = [0 1 0 1];
[t, z] = ode45(zprime,tspan,z0);

Pay attention