In this paper we apply the theory developed by Marsden, Ratiu, and Weinstein for the reduction of a Hamiltonian system defined on the cotangent bundle of a Lie group to a Hamiltonian system in the coalgebra of a semidirect product to study the motion of a self-gravitating homogeneous compressible ideal fluid with a variable ellipsoidal boundary, assuming that the motions are given by invertible linear transformations. The relation between the Lie–Poisson equations obtained and the classical Dyson equations is discussed, and the Hamiltonian structure for the homogeneous expansion of a free nonrotating ellipsoid is derived.
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© 2000 American Institute of Physics.
2000
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