The SharmaParthasarathy stochastic twobody problem
Abstract
We study the SharmaParthasarathy stochastic twobody problem introduced by Sharma and Parthasarathy in [“Dynamics of a stochastically perturbed twobody problem,” Proc. R. Soc. A 463, 9791003 (2007)]. In particular, we focus on the preservation of some fundamental features of the classical twobody 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 semimajor axis, the eccentricity, and the pericenter. We also derive a stochastic version of Gauss’s equations in the planar case.
 Authors:
 LMAP/Université de Pau, 64013 Pau (France)
 (France)
 SYRTE/Observatoire de Paris, 75014 Paris (France)
 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; TWOBODY PROBLEM
Citation Formats
Cresson, J., SYRTE/Observatoire de Paris, 75014 Paris, Pierret, F., and Puig, B. The SharmaParthasarathy stochastic twobody 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 SharmaParthasarathy stochastic twobody problem. United States. doi:10.1063/1.4906908.
Cresson, J., SYRTE/Observatoire de Paris, 75014 Paris, Pierret, F., and Puig, B. 2015.
"The SharmaParthasarathy stochastic twobody problem". United States.
doi:10.1063/1.4906908.
@article{osti_22403122,
title = {The SharmaParthasarathy stochastic twobody problem},
author = {Cresson, J. and SYRTE/Observatoire de Paris, 75014 Paris and Pierret, F. and Puig, B.},
abstractNote = {We study the SharmaParthasarathy stochastic twobody problem introduced by Sharma and Parthasarathy in [“Dynamics of a stochastically perturbed twobody problem,” Proc. R. Soc. A 463, 9791003 (2007)]. In particular, we focus on the preservation of some fundamental features of the classical twobody 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 semimajor 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 = 2015,
month = 3
}
DOI: 10.1063/1.4906908
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