GENERALIZED HAMILTONIAN STRUCTURES FOR SYSTEMS IN 3 DIMENSIONS WITH A RESCALABLE CONSTANT OF MOTION

The generalized Hamiltonian structures of several three-dimensional dynamical systems of interest in physical applications are considered. In general, Hamiltonians exist only for systems that possess at least one time-independent constant of motion. Systems with only time-dependent constants of motion may sometimes be rescaled and their constant of motion made time-independent. When this is possible, the transformed system may be cast in a generalized Hamiltonian formalism with non-canonical structure functions.