The Lie-Poisson Structure of the Symmetry Reduced Regularised n-Body Problem
Dynamical Systems
2018-02-01 v1 Mathematical Physics
math.MP
Abstract
This paper investigates the symmetry reduction of the regularised n-body problem. The three body problem, regularised through quaternions, is examined in detail. We show that for a suitably chosen symmetry group action the space of quadratic invariants is closed and the Hamiltonian can be written in terms of the quadratic invariants. The corresponding Lie-Poisson structure is isomorphic to the Lie algebra u(3,3). Finally, we generalise this result to the n-body problem for n>3.
Keywords
Cite
@article{arxiv.1408.2957,
title = {The Lie-Poisson Structure of the Symmetry Reduced Regularised n-Body Problem},
author = {Suntharan Arunasalam and Holger R. Dullin and Diana M. H. Nguyen},
journal= {arXiv preprint arXiv:1408.2957},
year = {2018}
}