Affiliation:
1. Hong Kong University of Science and Technology , Clear Water Bay, Kowloon, Hong Kong
Abstract
The phase space of the classical Kepler problem is incomplete, as certain Kepler motions do not continue indefinitely in time. To address this issue, a method called “regularization” was introduced in the 1960s and 1970s. While there are several versions of this scheme, the one developed by Ligon and Schaaf [Rep. Math. Phys. 9, 281–300 (1976)] is often preferred due to its global nature and lack of time reparameterization requirement. In this article, we present a new regularization method that is both global and requires no time reparameterization, while also exhibiting a higher degree of symmetry. Our method emphasizes symmetries over spaces and exhibits a duality similar to the compact-noncompact duality observed in symmetric spaces.
Subject
Mathematical Physics,Statistical and Nonlinear Physics