Deterministic and Random Perturbations of the Kepler Problem
Abstract
We investigate perturbations in the Kepler problem. We offer an overview of the dynamical system using Newtonian, Lagrangian and Hamiltonian Mechanics to build a foundation for analyzing perturbations. We consider the effects of a deterministic perturbation in the form of a first order relativistic correction which change bounded orbits from standard to precessing ellipses. We also consider the effects of stochastic perturbations with certain potentials and evaluate the analytical results of mean exit times using Monte Carlo simulations.
Cite
@article{arxiv.2206.08169,
title = {Deterministic and Random Perturbations of the Kepler Problem},
author = {Jesse Dimino},
journal= {arXiv preprint arXiv:2206.08169},
year = {2022}
}
Comments
Honors thesis submitted to Department of Mathematics of the College of Staten Island City University of New York in partial fulfillment of the requirements for the degree of Bachelor of Science in Mathematics with Honors. Signatures not included due to privacy concerns. Updated to correct certain figures and fixed citations