Dynamical Systems Seminar: Holger Dullin
A Lie-Poisson structure and integrator for the reduced N-Body problem
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Date and time:Ìý
Thursday, September 8, 2011 - 4:15pm
Abstract:Ìý
The general N-body problem is invariant under the symmetry group of translations, rotations, and Galilein boosts. The Hilber-Weyl invariants of this symmetry group can be represented by symmetric block-Laplacian matrices and we show that they satisfy a Lie-Poisson structure. Using this Lie-Poisson structure we construct a splitting integrator for the symmetry reduced N-body problem. For small N=3,4 this gives an efficient computational method, which is illustrated by computing the figure-8 choreography orbit in 3 steps.