2014/02/28 by Jacky Cresson, Frédéric Pierret, Bénédicte Puig · 1 citation
Physics and Astronomy · Mathematics · #math-ph #astro-ph.EP #math.MP
paper · pdf · doi:10.1063/1.4906908
published as J. Math. Phys. 56, 032701 (2015)
arxiv created 2014/10/03 · arxiv updated 2015/06/26
We study the Sharma-Parthasarathy stochastic two-body problem introduced by N. Sharma and H. Parthasarathy in \citesharma. 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.