Lie symmetries and adiabatic invariants for holonomic systems in event space

Zhang Yi

doi:10.7498/aps.56.3054

Abstract
The perturbations of Lie symmetries and adiabatic invariants for holonomic mechanical systems in event space are studied. Based on the definition of high-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for the system under the action of small disturbance is investigated, and a type of Hojman high-order adiabatic invariants of the system are obtained. The conditions for the existence of the adiabatic invariants and the form of the adiabatic invariants are given. An example is presented to illustrate the results.

Keywords:
event space /

symmetry /

perturbation /

adiabatic invariant
Authors and contacts
Zhang Yi

1.
苏州科技学院土木工程系，苏州 215011
References

Cited By

[1]	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
[2]	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
[3]	Lu Kai, Fang Jian-Hui, Zhang Ming-Jiang, Wang Peng. Noether symmetry and Mei symmetry of discrete holonomic system in phase space. Acta Physica Sinica, 2009, 58(11): 7421-7425. doi: 10.7498/aps.58.7421
[4]	Jia Li-Qun, Cui Jin-Chao, Luo Shao-Kai, Zhang Yao-Yu. Mei symmetry and Mei conserved quantity of Nielsen equations for nonholonomic systems of unilateral non-Chetaev’s type in the event space. Acta Physica Sinica, 2009, 58(4): 2141-2146. doi: 10.7498/aps.58.2141
[5]	Ding Ning, Fang Jian-Hui. A new type of Mei adiabatic invariant induced by perturbation to Mei symmetry for nonholonomic mechanical systems. Acta Physica Sinica, 2009, 58(11): 7440-7446. doi: 10.7498/aps.58.7440
[6]	Jia Li-Qun, Zheng Shi-Wang, Zhang Yao-Yu. Mei symmetry and Mei conserved quantity of nonholonomic systems of non-Chetaev’s type in event space. Acta Physica Sinica, 2007, 56(10): 5575-5579. doi: 10.7498/aps.56.5575
[7]	Jia Li-Qun, Zhang Yao-Yu, Zheng Shi-Wang. Hojman conserved quantities for systems with non-Chetaev nonholonomic constraints in the event space. Acta Physica Sinica, 2007, 56(2): 649-654. doi: 10.7498/aps.56.649
[8]	Luo Shao-Kai. A new type of non-Noether adiabatic invariants, i.e. adiabatic invariants of Lut zky type, for Lagrangian systems. Acta Physica Sinica, 2007, 56(10): 5580-5584. doi: 10.7498/aps.56.5580
[9]	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
[10]	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
[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
[13]	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
[14]	Zhang Yi. Symmetries and conserved quantities of mechanical systems with unilateral holonomic constraints in phase space. Acta Physica Sinica, 2005, 54(10): 4488-4495. doi: 10.7498/aps.54.4488
[15]	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
[16]	Fu Jing-Li, Chen Li-Qun, Xie Feng-Ping. Perturbation to the symmetries of relativistic Birkhoffian systems and the inver se problems. Acta Physica Sinica, 2003, 52(11): 2664-2670. doi: 10.7498/aps.52.2664
[17]	Zhang Yi, Mei Feng-Xiang. Perturbation to symmetries and adiabatic invariant for systems of generalized c lassical mechanics. Acta Physica Sinica, 2003, 52(10): 2368-2372. doi: 10.7498/aps.52.2368
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[20]	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

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Vol. 56, Issue 6 - 2007-03-20

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