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math.DS2014★ 7 cited
The Lie-Poisson Structure of the Symmetry Reduced Regularised n-Body Problem
Suntharan Arunasalam, Holger R. Dullin, Diana M. H. Nguyen
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…
math.DS2012★ 7 cited
The Lie-Poisson structure of the reduced n-body problem
Holger R. Dullin
The classical n-body problem in d-dimensional space is invariant under the Galilean symmetry group. We reduce by this symmetry group using the method of polynomial invariants. As a…