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Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type for Lagrange systems
罗绍凯, 陈向炜, 郭永新
2007 (11):
3176-3181.
doi: 10.1088/1009-1963/16/11/005
摘要
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Based on the invariance of differential equations under
infinitesimal transformations of group, Lie symmetries, exact
invariants, perturbation to the symmetries and adiabatic invariants
in form of non-Noether for a Lagrange system are presented. Firstly,
the exact invariants of generalized Hojman type led directly by Lie
symmetries for a Lagrange system without perturbations are given.
Then, on the basis of the concepts of Lie symmetries and higher
order adiabatic invariants of a mechanical system, the perturbation
of Lie symmetries for the system with the action of small
disturbance is investigated, the adiabatic invariants of generalized
Hojman type for the system are directly obtained, the conditions for
existence of the adiabatic invariants and their forms are proved.
Finally an example is presented to illustrate these results.
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