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Re: reflections on a neglected problem



At 12:05 PM on 4/2/97, <phys-l@mailer.uwf.edu> wrote:

Chip,

Do I read you correctly as saying that you have actually integrated the
equations of motion and obtained an algebraic expression relating the
final velocities to the charges and masses? If so, I'd be interested in
more information about the approach. Outside of a slowly growing number
of special cases, I have only been able to solve the general problem via
brute force numerical integration using Maple.

John

I didn't integrate the equations of motion, but I combined them and got
some things to cancel in the limit of large times. It works for the case
in which both charges are of the same sign. It might also work for the
case in which the signs are different, but the total energy is positive. I
haven't checked that.

One step was to switch to polar coordinates and follow the motion of the
imaginary point at (x,y) = (r, theta). I felt that I better understood the
way r, rdot, theta and thetadot should behave for large t. I'll provide
details if you wish.

Chip