On the n-body problem in R4
Abstract
Using geometric mechanics methods, we examine aspects of the dynamics of n mass points in R4 with a general pairwise potential. We investigate the central force problem, set up the n-body problem and discuss certain properties of relative equilibria. We describe regular n-gons in R4, and when the masses are equal we determine the invariant manifold of motions with regular n-gon configurations. In the case n = 3, we reduce the dynamics to a 6 d.f. system and we show that for generic potentials and momenta, relative equilibria with equilateral configuration are unstable.
This article is part of the theme issue `Topological and geometrical aspects of mass and vortex dynamics'.- Publication:
-
Philosophical Transactions of the Royal Society of London Series A
- Pub Date:
- November 2019
- DOI:
- 10.1098/rsta.2019.0018
- Bibcode:
- 2019RSPTA.37790018S