论文标题
开普勒问题的确定性和随机扰动
Deterministic and Random Perturbations of the Kepler Problem
论文作者
论文摘要
我们研究开普勒问题中的扰动。我们使用牛顿，拉格朗日和哈密顿式力学来概述动态系统，以建立分析扰动的基础。我们考虑以一阶相对论校正形式确定性扰动的效果，该校正将有限的轨道从标准轨道变为进攻椭圆。我们还考虑了具有某些潜力的随机扰动的影响，并使用蒙特卡洛模拟评估了平均出口时间的分析结果。
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.
