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Title: The Sharma-Parthasarathy stochastic two-body problem

Abstract

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.

Authors:
 [1];  [2];  [3];  [4]
  1. LMAP/Université de Pau, 64013 Pau (France)
  2. (France)
  3. SYRTE/Observatoire de Paris, 75014 Paris (France)
  4. IPRA/Université de Pau, 64013 Pau (France)
Publication Date:
OSTI Identifier:
22403122
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 3; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTERIZED SIMULATION; EQUATIONS; HAMILTONIANS; INTEGRALS; STOCHASTIC PROCESSES; TWO-BODY PROBLEM

Citation Formats

Cresson, J., SYRTE/Observatoire de Paris, 75014 Paris, Pierret, F., and Puig, B. The Sharma-Parthasarathy stochastic two-body problem. United States: N. p., 2015. Web. doi:10.1063/1.4906908.
Cresson, J., SYRTE/Observatoire de Paris, 75014 Paris, Pierret, F., & Puig, B. The Sharma-Parthasarathy stochastic two-body problem. United States. doi:10.1063/1.4906908.
Cresson, J., SYRTE/Observatoire de Paris, 75014 Paris, Pierret, F., and Puig, B. Sun . "The Sharma-Parthasarathy stochastic two-body problem". United States. doi:10.1063/1.4906908.
@article{osti_22403122,
title = {The Sharma-Parthasarathy stochastic two-body problem},
author = {Cresson, J. and SYRTE/Observatoire de Paris, 75014 Paris and Pierret, F. and Puig, B.},
abstractNote = {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.},
doi = {10.1063/1.4906908},
journal = {Journal of Mathematical Physics},
number = 3,
volume = 56,
place = {United States},
year = {Sun Mar 15 00:00:00 EDT 2015},
month = {Sun Mar 15 00:00:00 EDT 2015}
}