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Perturbation to symmetries and adiabatic invariants of a type of nonholonomic singular system

Keywords: nonholonomic singular system,perturbation to symmetry,exact invariant,adiabatic invariant
对称扰动
,绝热不变量,异常不完整系统,哈密顿系统,拉格朗日函数,数学物理方法

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Abstract:

Based on the theory of symmetries and conserved quantities, the perturbation to the symmetries and adiabatic invariants of a type of nonholonomic singular system are discussed. Firstly, the concept of higher order adiabatic invariants of the system is proposed. Secondly, the conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are given. Thirdly, we study the inverse problems of the perturbation to symmetries of the system. An example is presented to illustrate these results.

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