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arXiv · 1402.1752

The Sharma-Parthasarathy stochastic two-body problem

Jacky Cresson·Frédéric Pierret·Bénédicte Puig
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Abstract

We study the Sharma-Parthasarathy stochastic two-body problem introduced by N. Sharma and H. Parthasarathy in \cite{sharma}. In particular, we focus on the preservation of some fundamental features of the classical two-body problem like the Hamiltonian structure and first integrals in the stochastic case. Numerical simulations are performed which illustrate the dynamical behaviour of the osculating elements as the semi-major axis, the eccentricity and the pericenter. We also derive a stochastic version of Gauss's equations in the planar case.

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Jacky Cresson, Frédéric Pierret, Bénédicte Puig. 2014-10-03. The Sharma-Parthasarathy stochastic two-body problem. https://doi.org/10.1063/1.4906908

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