Re: [Phys-l] Rocket Science

[John Denker <jsd@av8n.com>]

Carl Mungan wrote:

> r(1+r*r)(ddr) = (2+r*r)(dr)(dr) + r*r[1-(r/r0)^4]

Is this really a rocket science problem?
Is it even a physics problem?
If it's just a math puzzle, that's OK, but you'll attract
more attention if you can put some physical interpretation
on it.

>  How can I prove mathematically 
> that the orbits aren't closed for any positive values of the two 
> initial parameters?

You can't prove that, because there are *some* parameter values that
do produce closed orbits.

For starters, if you set r(t) = const = r0 and dr/dtheta = 0, the
particle moves around in a nice closed circle with any dtheta/dt
you like.

The fact that the motion is insensitive to dtheta/dt makes me
suspect that this is not an orbital dynamics problem.