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Title: A SYMPLECTIC INTEGRATOR FOR HILL'S EQUATIONS

Abstract

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.

Authors:
;  [1]; ;  [2]
  1. Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195 (United States)
  2. Department of Astronomy, University of Maryland, Computer and Space Sciences Building, Stadium Drive College Park, MD 20742 (United States), E-mail: trq@astro.washington.edu
Publication Date:
OSTI Identifier:
21301345
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astronomical Journal (New York, N.Y. Online); Journal Volume: 139; Journal Issue: 2; Other Information: DOI: 10.1088/0004-6256/139/2/803; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; APPROXIMATIONS; ASTROPHYSICS; EXTRAPOLATION; HILL EQUATION; ORBITS

Citation Formats

Quinn, Thomas, Barnes, Rory, Perrine, Randall P., and Richardson, Derek C. A SYMPLECTIC INTEGRATOR FOR HILL'S EQUATIONS. United States: N. p., 2010. Web. doi:10.1088/0004-6256/139/2/803; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Quinn, Thomas, Barnes, Rory, Perrine, Randall P., & Richardson, Derek C. A SYMPLECTIC INTEGRATOR FOR HILL'S EQUATIONS. United States. doi:10.1088/0004-6256/139/2/803; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Quinn, Thomas, Barnes, Rory, Perrine, Randall P., and Richardson, Derek C. 2010. "A SYMPLECTIC INTEGRATOR FOR HILL'S EQUATIONS". United States. doi:10.1088/0004-6256/139/2/803; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
@article{osti_21301345,
title = {A SYMPLECTIC INTEGRATOR FOR HILL'S EQUATIONS},
author = {Quinn, Thomas and Barnes, Rory and Perrine, Randall P. and Richardson, Derek C.},
abstractNote = {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.},
doi = {10.1088/0004-6256/139/2/803; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},
journal = {Astronomical Journal (New York, N.Y. Online)},
number = 2,
volume = 139,
place = {United States},
year = 2010,
month = 2
}
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