The Sharma-Parthasarathy stochastic two-body problem

Journal Article · Sun Mar 15 00:00:00 EDT 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4906908· OSTI ID:22403122

Cresson, J. ^[1]; Pierret, F. ^[2]; Puig, B. ^[3]

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1. LMAP/Université de Pau, 64013 Pau (France)
2. SYRTE/Observatoire de Paris, 75014 Paris (France)
3. IPRA/Université de Pau, 64013 Pau (France)

We study the Sharma-Parthasarathy stochastic two-body problem introduced by Sharma and Parthasarathy in [“Dynamics of a stochastically perturbed two-body problem,” Proc. R. Soc. A 463, 979-1003 (2007)]. 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.

• OSTI ID: 22403122
• Journal Information: Journal of Mathematical Physics, Vol. 56, Issue 3; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMPUTERIZED SIMULATION
EQUATIONS
HAMILTONIANS
INTEGRALS
STOCHASTIC PROCESSES
TWO-BODY PROBLEM