Abstract
Using geometric mechanics methods, we examine aspects of the dynamics ofnmass points inR4with a general pairwise potential. We investigate the central force problem, set up then-body problem and discuss certain properties of relative equilibria. We describe regularn-gons inR4, and when the masses are equal we determine the invariant manifold of motions with regularn-gon configurations. In the casen = 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’.
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Schedule a callMore From: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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