The Euler-Poincare Equations and Semidirect Products with Applications to Continuum Theories

D. D. Holm, J. E. Marsden, T. S. Ratiu

We study Euler-Poincare systems (i.e., the Lagrangian analogue of Lie-Poisson Hamiltonian systems) defined on semidirect product Lie algebras. We first give a derivation of the Eul…