  Hill's equations are an approximation that is useful in a number of areas of
astrophysics including planetary rings and planetesimal disks. We derive a
symplectic method for integrating Hill's equations based on a generalized
leapfrog. This method is implemented in the parallel N-body code, PKDGRAV and
tested on some simple orbits. The method demonstrates a lack of secular changes
in orbital elements, making it a very useful technique for integrating Hill's
equations over many dynamical times. Furthermore, the method allows for
efficient collision searching using linear extrapolation of particle positions.
