N-body integrators for planets in binary star systems
Abstract
Symplectic integrators are the tool of choice for many researchers studying dynamical systems because of their good long-term energy conservation properties. For systems with a dominant central mass, symplectic integrators are also highly efficient. In this chapter, I describe the theory of symplectic integrators in terms of Lie series. I show how conventional symplectic algorithms have been adapted for use in binary-star systems to study problems such as the dynamical stability of multi-planet systems and the accretion of planets from planetesimals. This is achieved by devising new coordinate systems for the wide-binary and close-binary cases separately. I show how the performance of these algorithms can be improved at little extra cost using symplectic correctors. Finally, I discuss drawbacks of these algorithms, in particular in dealing with close encounters with one or both members of the binary, and the prospects for overcoming these problems.
Cite
@article{arxiv.0705.3223,
title = {N-body integrators for planets in binary star systems},
author = {John E. Chambers},
journal= {arXiv preprint arXiv:0705.3223},
year = {2007}
}