A SYMPLECTIC INTEGRATOR FOR HILL'S EQUATIONS

摘要

Hill's equations are an approximation that is useful in a number of areas of astrophysics including planetary ringsand planetesimal disks. We derive a symplectic method for integrating Hill's equations based on a generalizedleapfrog. 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 forintegrating Hill's equations over many dynamical times. Furthermore, the method allows for efficient collisionsearching using linear extrapolation of particle positions.