Decomposing Euler–Poincaré Flow on the Space of Hamiltonian Vector Fields

The main result of this paper is a matched-pair decomposition the space symmetric contravariant tensors TQ. From procedure two complementary Lie subalgebras TQ under mutual interaction arise. Introducing lift operator, matched pair Hamiltonian vector fields determined. According to realization, Euler–Poincaré flows on such spaces are decomposed into subdynamics: one formulation isentropic fluid flows, and other corresponds with equations order n⩾2.