Solving odes (restricted 3 body problems)

I have been trying to solve these equations -

d2x dt2 = 2 dy dt + x− M(x + E) r3 E − E(x−M) r3 M

d2y dt2 = −2 dx dt + y− My r3 E − Ey r3 M

z1 = x, z2 = dx dt , z3 = y, and z4 = dy dt

but keep getting these errors:-

Unrecognized function or variable 'rE'.

Error in secodef (line 4) zprime=[z(2);2*z(4)+z(1)-((M*(z(1)+E))/rE^3)-((E*(z(1)-M))/rM^3);z(4);-2*z(2)+z(3)-((M*z(3))/rE^3)-((E*z(3))/rM^3)];

Error in odearguments (line 90) f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 115) odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in trial1 (line 13) [t,z] = ode45(@secodef,tspan,Z);

what do I do?

Answer 1

[darova]

Variables rE and rM should be in the function

[Aneesa Shahbaz]

After I move rE and rM into the function I get this as a result:

Not enough input arguments.

Error in secodef (line 8)

rE = sqrt((z(1)+E)^2 +z(3)^2);

[darova]

Can you attach the function?

[Aneesa Shahbaz]

The function is this but coming up with the result:

Not enough input arguments.

Error in secodef (line 8)

rE = sqrt((z(1)+E)^2 +z(3)^2);

What do I do?

[darova]

Works for me

>> secodef(1,[1 2 3 4])
ans =
    2.0000
    8.9685
    4.0000
   -1.0947

[Aneesa Shahbaz]

Thank you, I got it to work.

However i am trying to plot a graph but the plot is empty and only 2 points can be shown the earth and the moon.

What do I do?

[darova]

Please see the image i made for you. I think there is some connection

[Aneesa Shahbaz]

I understand that z1 = x and z3 = y.

But I don't know what to do to get the graph.

[darova]

Do you know how to select columns?

[Aneesa Shahbaz]

Not really no