Gauss's method for secular dynamics, softened
Abstract
We show that the algorithm proposed by Gauss to compute the secular evolution of gravitationally interacting Keplerian rings extends naturally to softened gravitational interactions. The resulting tool is ideal for the study of the secular dynamical evolution of nearly Keplerian systems such as stellar clusters surrounding black holes in galactic nuclei, cometary clouds, or planetesimal discs. We illustrate its accuracy, efficiency and versatility on a variety of configurations. In particular, we examine a secularly unstable unstable system of counter-rotating disks, and follow the unfolding and saturation of the instability into a global, uniformly precessing, lopsided (m=1) mode.
Cite
@article{arxiv.0811.2812,
title = {Gauss's method for secular dynamics, softened},
author = {J. R. Touma and S. Tremaine and M. V. Kazandjian},
journal= {arXiv preprint arXiv:0811.2812},
year = {2010}
}
Comments
28 pages, 11 figures; minor changes to text and figures. To be published in MNRAS