PERTURBATION TO THE SYMMETRIES AND ADIABATIC INVARIANTS OF HOLONOMIC VARIABLE MASS SYSTEMS

The perturbation problem of symmetries for the holonomic variable mass systems under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of adiabatic invariants and the conditions for their existence are given. Then the corresponding inverse problem is studied. Finally an example is presented to illustrate these results.