Euler-Poisson equations on Lie algebras and the N-dimensional heavy rigid body.
The classical Euler-Poisson equations describing the motion of a heavy rigid body about a fixed point are generalized to arbitrary Lie algebras as Hamiltonian systems on coad-joint orbits of a tangent bundle Lie group. the N-dimensional Lagrange and symmetric heavy top are thereby shown to be completely integrable.
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Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109.