Hill's Equations

There's a name for objects in "toroidal orbits" - Hill's equations, in the "Hill's frame."

This paper:

shows the three equations below, and claims they are found here:

but I don't see them in that three equation form. I suspect these are versions from a more recent paper.

\ddot x - 2 \omega \dot y - 3 \omega^2 x ~=~ f_x ~~~~ x is the radial direction

\ddot y + 2 \omega \dot x ~=~ f_y ~~~~~~~~~~~~~~~ y is the orbital direction

\ddot z + \omega^2 z ~=~ f_z ~~~~~~~~~~~~~~~~ z is perpendicular to the orbital plane. Right handed triad mentioned in Burns, the equation works with left triad, too.

HillsEquations (last edited 2016-04-14 03:22:38 by KeithLofstrom)