Reduced Hamiltonian Dynamics for a Rigid Body Coupled to a Moving Point Mass

Abstract

Three equivalent reduced-dimensional Hamiltonian systems that model a rigid body in a perfect fluid coupled to am oving-mass particle are presented. These Hamiltonian systems describe the dynamics of an underwater vehicle with a moving-mass actuator or a flexible internal appendage. The systems include, as a special case, models for a spacecraft coupled to a moving mass. The Hamiltonian models are noncanonical; the structure of Hamilton’s equations is defined by the Poisson tensor, a generalization of the symplectic matrix from classical mechanics. The three models presented trade complexity of the generalized inertia tensor for complexity of the Poisson tensor. One model has a highly coupled inertia tensor and a block-diagonal Poisson tensor, whereas another has a highly coupled Poisson tensor and a block-diagonal inertia tensor. Two cases are considered. The first is that of an unconstrained mass particle. The second is that of a mass particle constrained to move in a linear track. Examples are included to illustrate the use of these models for nonlinear stability analysis.