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# 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} }

- 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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