How to solve motion equation in symbolic way?

Hi guys,

I have the following equation (motion eq)

m*r''= f(x,y)

f(x,y)=cos(r)*[((3*x*y)-x^3) /(r^4)- (x^3-4*x*y^2) /(r^7)];

where r'' - second derivative with respect to time, r =sqrt(x(t)^2+y(t)^2), m-const, x0 and y0 at initial time are given.

How can I solve this eq in a symbolic way and plot r(t)?

Thank you!

[John D'Errico]

Nobody can tell you. Why not? Because nobody knows the function f(x,y). Perhaps you, but you have kept that a secret.

[Ivan]

Hi John,

Here is the function..

f(x,y)=cos(r)*[((3*x*y)-x^3) /(r^4)- (x^3-4*x*y^2) /(r^7)];

thx for comments!

[John D'Errico]

Hmm. f(x,y) is a bit messy. That makes it unlikely in my eyes that an analytical solution exists at all. Unless of course this is homework, in which case if you were told to find the analytical solution, then one will surely exist, despite the messiness of f(x,y).

In that case, the solution would seem to be to use a tool like ODE45 to solve it. I wonder if the solution should most easily arrive by converting the (x,y) coordinate system into the complex plane, so now you have the motion as X(t) = x(t) + i*y(t), with X(0)=x0+i*y0.