Exact Invariants and Adiabatic Invariants of Nonholonomic Variable Mass Systems

By the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic variable mass systems are studied. The perturbation problem of symmetries for the nonholonomic variable mass systems under small excitation is discussed. The concept of high order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.