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物理学报  2007 

A new type of non-Noether adiabatic invariants, i.e. adiabatic invariants of Lut zky type, for Lagrangian systems

Keywords: analytical mechanics,Lagrangian system,symmetry,perturbation

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The perturbation of Lie symmetries and new non-Noether adiabatic invariants for the Lagrangian system are studied. The exact invariants of Lutzky type arising f rom the Lie symmetries of Lagrangian system without perturbation are given. Base d on the definition of high-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for Lagrangian system under the action of smal l disturbances is investigated, and a type of Lutzky adiabatic invariants of the system are obtained. An example is given to illustrate the application of the m ethod and results.


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