Circularization under radial inverse-square drag (source code)

= Circularization under radial inverse-square drag
{title2=$r\longrightarrow h^2/p,\quad\dot E=-k\dot r^2/r^2$}

A bounded trajectory in the <damped Binet equation> with nonzero <angular momentum> asymptotically becomes circular. Energy loss is nonnegative in magnitude and vanishes only for zero radial velocity. The centrifugal effective <potential energy> excludes collision; bounded radius forces indefinitely increasing forward angular distance, so the reciprocal-radius oscillation decays. Escaping trajectories are excluded by the boundedness hypothesis.