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

@article{Ratiu1981EulerPoissonEO,
  title={Euler-Poisson equations on Lie algebras and the N-dimensional heavy rigid body.},
  author={Tudor Ratiu},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  year={1981},
  volume={78 3},
  pages={1327-8}
}
  • Tudor Ratiu
  • Published 1981 in
    Proceedings of the National Academy of Sciences…
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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