# 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:

- 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; 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}

}

DOI: 10.1063/1.4906908

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