Semidirect Products and Reduction in Mechanics

  title={Semidirect Products and Reduction in Mechanics},
  author={Jerrold E. Marsden and Tudor S. Ratiu and Alan Weinstein and Guillemin Greene and H Jodaa Holm and Marsden Kupershmidt and Ratiu Morrison},
This paper shows how to reduce a Hamiltonian system on the cotangent bundle of a Lie group to a Hamiltonian system in the dual of the Lie algebra of a semidirect product. The procedure simplifies. unifies, and extends work of Greene, Guillemin, Holm, Holmes, Kupershmidt, Marsden, Morrison, Ratiu, Sternberg and others. The heavy top, compressible fluids, magnetohydrodynamics, elasticity, the Maxwell-Vlasov equations and multi fluid plasmas are presented as examples. Starting with Lagrangian… CONTINUE READING
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