Attracting and repelling 2-body problems on a family of surfaces of constant curvature

Montaldi, James and García-Naranjo, Luis C. (2019) Attracting and repelling 2-body problems on a family of surfaces of constant curvature. [MIMS Preprint]

[img] Text
family.pdf

Download (652kB)

Abstract

We first provide a classification of the pure rotational motion of 2 particles on a sphere interacting via a repelling potential. This is achieved by providing a simple geometric equivalence between repelling particles and attracting particles, and relying on previous work on the similar classification for attracting particles. The second theme of the paper is to study the 2-body problem on a surface of constant curvature treating the curvature as a parameter, and with particular interest in how families of relative equilibria and their stability behave as the curvature passes through zero and changes sign. We consider two cases: firstly one where the particles are always attracting throughout the family, and secondly where they are attracting for negative curvature and repelling for positive curvature, interpolated by no interaction when the curvature vanishes. Our analysis clarifies the role of curvature in the existence and stability of relative equilibria.

Item Type: MIMS Preprint
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 70 Mechanics of particles and systems
Depositing User: Dr James Montaldi
Date Deposited: 05 Jun 2019 07:39
Last Modified: 05 Jun 2019 07:39
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2713

Actions (login required)

View Item View Item