Unifying the Hyperbolic and Spherical 2-Body Problem with Biquaternions
Mathematical Physics
2020-12-23 v1 Dynamical Systems
math.MP
Abstract
The 2-body problem on the sphere and hyperbolic space are both real forms of holomorphic Hamiltonian systems defined on the complex sphere. This admits a natural description in terms of biquaternions and allows us to address questions concerning the hyperbolic system by complexifying it and treating it as the complexification of a spherical system. In this way, results for the 2-body problem on the sphere are readily translated to the hyperbolic case. For instance, we implement this idea to completely classify the relative equilibria for the 2-body problem on hyperbolic 3-space for a strictly attractive potential.
Cite
@article{arxiv.2012.12166,
title = {Unifying the Hyperbolic and Spherical 2-Body Problem with Biquaternions},
author = {Philip Arathoon},
journal= {arXiv preprint arXiv:2012.12166},
year = {2020}
}
Comments
15 pages