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Abstract
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.

Keywords:
analytical mechanics/

Lagrangian system/

symmetry/

perturbation
Authors and contacts
Luo Shao-Kai

1.
References

Cited By

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[2]	Hu Chu-Le.Lie symmetries and Hojman conserved quantities of one kind of differential equations of motion of nonholonomic systems. Acta Physica Sinica, 2007, 56(7): 3675-3677.doi:10.7498/aps.56.3675
[3]	Zhang Yi.Perturbation of symmetries and Hojman adiabatic invariants of discrete mechanical systems in the phase space. Acta Physica Sinica, 2007, 56(4): 1855-1859.doi:10.7498/aps.56.1855
[4]	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
[5]	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
[6]	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
[7]	Zhang Yi.Non-Noether conserved quantities for systems with unilateral non-Chetaev nonholonomic constraints. Acta Physica Sinica, 2006, 55(2): 504-510.doi:10.7498/aps.55.504
[8]	Zhang Yi, Fan Cun-Xin, Mei Feng-Xiang.Perturbation of symmetries and Hojman adiabatic invariants for Lagrangian system. Acta Physica Sinica, 2006, 55(7): 3237-3240.doi:10.7498/aps.55.3237
[9]	Fang Jian-Hui, Peng Yong, Liao Yong-Pan.On Mei symmetry of Lagrangian system and Hamiltonian system. Acta Physica Sinica, 2005, 54(2): 496-499.doi:10.7498/aps.54.496
[10]	Xu Xue-Jun, Mei Feng-Xiang, Qin Mao-Chang.Hojman conserved quantity for a holonomic system in the event space. Acta Physica Sinica, 2005, 54(3): 1009-1014.doi:10.7498/aps.54.1009
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[19]	QIAO YONG-FEN, LI REN-JIE, ZHAO SHU-HONG.SYMMETRY AND INVARIANT IN GENERALIZED MECHANICAL SYSTEMS IN THE HIGH-DIMENSIONAL EXTENDED PHASE SPACE. Acta Physica Sinica, 2001, 50(5): 811-815.doi:10.7498/aps.50.811
[20]	ZHANG HONG-BIN.NOETHER’S THEORY OF BIRKHOFF SYSTEMS WITH UNILATERAL CONSTRAINTS. Acta Physica Sinica, 2001, 50(10): 1837-1841.doi:10.7498/aps.50.1837

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Vol. 56, Issue 10 - 2007-05-20

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