Hamiltonian mechanics and nonlinear dynamics of a body subject to time-varying gyroscopic and potential forces

摘要

We consider the planar dynamics of a body under the simultaneous influence of a force given by the spatial gradient of a potential function and a force that remains perpendicular to the body's translational velocity. Either force can vary with time. We describe a physical example of such a system and analyze the structure of the underlying equations of motion, demonstrating that they exemplify a special class of almost Hamiltonian systems. We show that when the potential function varies periodically with time, the momentum of the body can evolve chaotically.