Hill equations
= Hill equations
{c}
The unforced planar <equation of motion in a rotating frame> near a circular <Kepler orbit> has components $\ddot x-2n\dot y-3n^2x=0$ and $\ddot y+2n\dot x=0$. They describe <epicyclic motion> and <Keplerian shear>; mutual gravity adds close-encounter forcing.