Perturbation of symmetries and Hojman adiabatic invariants for Lagrangian system

Zhang Yi; Fan Cun-Xin; Mei Feng-Xiang

doi:10.7498/aps.55.3237

Abstract
The perturbation of symmetries and adiabatic invariants for Lagrangian system are studied. The exact invariants introduced by the Lie symmetries of Lagrangian system without perturbation are given. Based on the definition of high-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for Lagrangian system with the action of small disturbance is investigated, and a type of Hojman adiabatic invariants of the system are obtained. An example is given to illustrate the application of the results.

Keywords:
Lagrangian system /

symmetry /

perturbation /

adiabatic invariant
Authors and contacts
Zhang Yi²,

Fan Cun-Xin²,

Mei Feng-Xiang¹

(1)北京理工大学力学系，北京 100081; (2)苏州科技学院土木工程系，苏州 215011
References

Cited By

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[2]	Chen Ju, Zhang Yi. Perturbation to Noether symmetries and adiabatic invariants for Birkhoffian systems based on El-Nabulsi dynamical models. Acta Physica Sinica, 2014, 63(10): 104501. doi: 10.7498/aps.63.104501
[3]	Zhang Yi. Perturbation to Noether symmetries and adiabatic invariants for nonconservative dynamic systems. Acta Physica Sinica, 2013, 62(16): 164501. doi: 10.7498/aps.62.164501
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[9]	Zhang Yi. Lie symmetries and adiabatic invariants for holonomic systems in event space. Acta Physica Sinica, 2007, 56(6): 3054-3059. doi: 10.7498/aps.56.3054
[10]	Jing Hong-Xing, Li Yuan-Cheng, Xia Li-Li. Perturbation of Lie symmetries and a type of generalized Hojman adiabatic invariants for variable mass systems with unilateral holonomic constraints. Acta Physica Sinica, 2007, 56(6): 3043-3049. doi: 10.7498/aps.56.3043
[11]	Xia Li-Li, Li Yuan-Cheng. Perturbation to symmetries and adiabatic invariant for nonholonomic controllable mechanical system in phase place. Acta Physica Sinica, 2007, 56(11): 6183-6187. doi: 10.7498/aps.56.6183
[12]	Zhang Yi. A new type of adiabatic invariants for Birkhoffian system. Acta Physica Sinica, 2006, 55(8): 3833-3837. doi: 10.7498/aps.55.3833
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[15]	Zhang Yi, Mei Feng-Xiang. Effects of non-conservative forces and nonholonomic constraints on Noether symmetries of a Lagrange system. Acta Physica Sinica, 2004, 53(3): 661-668. doi: 10.7498/aps.53.661
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Vol. 55, Issue 7 - 2006-04-05

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Perturbation of symmetries and Hojman adiabatic invariants for Lagrangian system

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