Semidirect product reduction theory: a user's guide
  Here we carry out computations that help clarify the Lagrangian and Hamiltonian structure of compressible flow. The intent is to be pedagogical and rigorous, providing concrete examples of the theory outlined in Holm, Marsden, and Ratiu [1998] and Marsden, Ratiu, and Weinstein [1984]. 
H. S. Bhat