Stochastic Gauss Equations
Earth and Planetary Astrophysics
2015-11-04 v4
Abstract
We derive the equations of celestial mechanics governing the variations of the orbital elements under a stochastic perturbation generalizing the classical Gauss equations. Explicit formulas are given for the semi-major axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle and the mean anomaly which are express in term of the angular momentum vector per unit of mass and the energy per unit of mass. Together, these formulas are called the \emph{stochastic Gauss equations} and they are illustrated numerically on an example from satellite dynamics.
Cite
@article{arxiv.1402.1758,
title = {Stochastic Gauss Equations},
author = {Frédéric Pierret},
journal= {arXiv preprint arXiv:1402.1758},
year = {2015}
}