A Symplectic Integrator for Hill's Equations

Details A Symplectic Integrator for Hill's Equations A Symplectic Integrator for Hill's Equations

2009-08-17

arxiv.org/abs/0908.2269v2

Astronomy and Astrophysics

Astrophysics

Earth and Planetary Astrophysics

15 pages, 2 figures; minor revisions; accepted for publication in the Astronomical Journal

Scientific paper

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.

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