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arXiv · 1207.5883

The Lie-Poisson structure of the reduced n-body problem

Holger R. Dullin
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Abstract

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 result we obtain a reduced system with a Lie-Poisson structure which is isomorphic to sp(2n-2), independently of d. The reduction preserves the natural form of the Hamiltonian as a sum of kinetic energy that depends on velocities only and a potential that depends on positions only. Hence we proceed to construct a Poisson integrator for the reduced n-body problem using a splitting method.

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Holger R. Dullin. 2012-07-25. The Lie-Poisson structure of the reduced n-body problem. https://doi.org/10.1088/0951-7715%2F26%2F6%2F1565

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