Abstract
Based on the theory of Lie symmetries andconserved quantities, the exact invariants and adiabatic invariants ofnonholonomic system in terms of quasi-coordinates are studied. Theperturbation to symmetries for the nonholonomic system in terms ofquasi-coordinates under small excitation is discussed. The concept ofhigh-order adiabatic invariant is presented, and the forms of exactinvariants and adiabatic invariants as well as the conditions for theirexistence are given. Then the corresponding inverse problem is studied.
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