Abstract
This paper investigates the symmetry reduction of the regularized n-body problem. The three body problem, regularized through quaternions, is examined in detail. We show that for a suitably chosen symmetry group action the space of quadratic invariants is closed and the Hamiltonian can be written in terms of the quadratic invariants. The corresponding Lie–Poisson structure is isomorphic to the Lie algebra . Finally, we generalize this result to the n-body problem for .
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More From: Journal of Physics A: Mathematical and Theoretical
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