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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1981 Mar;78(3):1327–1328. doi: 10.1073/pnas.78.3.1327

Euler-Poisson equations on Lie algebras and the N-dimensional heavy rigid body

Tudor Ratiu 1
PMCID: PMC319122  PMID: 16592990

Abstract

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.

Keywords: Hamiltonian mechanics, completely integrable systems

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