solving odes (resiscted 3 body problem)

ive 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 this error

Error using vertcat Dimensions of matrices being concatenated are not consistent.

Error in secodef (line 10) 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 solode (line 5) [t,z] = ode45(@secodef,xspan,z0);

what do?

Answer 1

[James Tursa]

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.

[del]

thank you so much this really helped