Moser Regularization of a Stochastically Perturbed Kepler Problem

2025/04/20 by Saha, Archishman
#60H10 #70F16 (Secondary) #70L10 (Primary) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2504.14442

Abstract

We consider a stochastic Kepler problem perturbed by a Hamiltonian noise affecting the angular momentum vector. We show that the angular momentum and the Laplace-Runge-Lenz vectors are conserved in magnitude and as a consequence, the distance and speed of the particle follow deterministic dynamics. Further, in a procedure similar to Moser's regularization, we transform the stochastic Kepler problem to obtain its dynamics as a stochastic geodesic flow on a 3-sphere.

Citations

• Semimartingale driven mechanics and reduction by symmetry for stochastic and dissipative dynamical systems
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• Semi-martingale driven variational principles
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• Stochastic Hamiltonian dynamical systems
• Stochastic embedding of dynamical systems
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• Dynamical Theories of Brownian Motion
• Derivation of the Schrödinger Equation from Newtonian Mechanics

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• Most Probable KAM Tori in Stochastic Hamiltonian Systems