How to solve motion equation in symbolic way?

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Ivan
Ivan 2019-11-6
评论： John D'Errico 2019-11-6
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!
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Ivan
Ivan 2019-11-6
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
John D'Errico 2019-11-6
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.

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