Non－Noether conserved quantity of a general form for mechanical systems with variable mass

Fang Jian－Hui; Liao Yong－Pan; Zhang Jun

doi:10.7498/aps.53.4037

Abstract
In this paper, we study the non-Noether conserved quantity of Lie symmetry for m echanical systems with variable mass under a general infinitesimal transformatio n. The Hojman theorem is further generalized. The non-Noether conserved qu antity o f a general form for mechanical systems with variable mass is obtained. An examp le is given to illustrate the application of the result.

Keywords:
variable mass system /

general infinitesimal transformation /

non_Noether conserve d quantity
Authors and contacts
Fang Jian－Hui²,

Liao Yong－Pan¹,

Zhang Jun²

(1)河西学院物理系，张掖　734000; (2)石油大学(华东)物理科学与技术学院,东营　257061
References

Cited By

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[2]	Ge Wei-Kuan, Zhang Yi, Lou Zhi-Mei. Infinitesimal canonical transformation and integral for a generalized Birkhoff system. Acta Physica Sinica, 2012, 61(14): 140204. doi: 10.7498/aps.61.140204
[3]	Chen Xiang-Wei, Zhao Yong-Hong, Liu Chang. Conformal invariance and conserved quantity for holonomic mechanical systems with variable mass. Acta Physica Sinica, 2009, 58(8): 5150-5154. doi: 10.7498/aps.58.5150
[4]	Xia Li-Li, Li Yuan-Cheng, Wang Xian-Jun. Non-Noether conserved quantities for nonholonomic controllable mechanical systems with relativistic rotational variable mass. Acta Physica Sinica, 2009, 58(1): 28-33. doi: 10.7498/aps.58.28
[5]	Huang Xiao-Hong, Zhang Xiao-Bo, Shi Shen-Yang. The Mei symmetry of discrete difference sequence mechanical system with variable mass. Acta Physica Sinica, 2008, 57(10): 6056-6062. doi: 10.7498/aps.57.6056
[6]	Liu Yang-Kui, Fang Jian-Hui. Two types of conserved quantities of Lie-Mei symmetry for a variable mass system in phase space. Acta Physica Sinica, 2008, 57(11): 6699-6703. doi: 10.7498/aps.57.6699
[7]	Xia Li-Li, Li Yuan-Cheng. Non-Noether conserved quantity for relativistic nonholonomic controllable mechanical system with variable mass. Acta Physica Sinica, 2008, 57(8): 4652-4656. doi: 10.7498/aps.57.4652
[8]	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
[9]	Qiao Yong-Fen, Zhao Shu-Hong. Form invariance and non-Noether conserved quantity of generalized Raitzin’s canonical equations of non-conservative system. Acta Physica Sinica, 2006, 55(2): 499-503. doi: 10.7498/aps.55.499
[10]	Zhang Peng-Yu, Fang Jian-Hui. Lie symmetry and non-Noether conserved quantities of variable mass Birkhoffian system. Acta Physica Sinica, 2006, 55(8): 3813-3816. doi: 10.7498/aps.55.3813
[11]	Ge Wei-Kuan. Effects of mass variation on form invariance and conserved quantity of mechanical systems. Acta Physica Sinica, 2005, 54(6): 2478-2481. doi: 10.7498/aps.54.2478
[12]	Xu Xue-Jun, Mei Feng-Xiang, Qin Mao-Chang. A nonNoether conserved quantity constructed using form invariance for Nielsen equation of a non-conservativemechanical system. Acta Physica Sinica, 2004, 53(12): 4021-4025. doi: 10.7498/aps.53.4021
[13]	Luo Shao-Kai, Guo Yong-Xin, Mei Feng-Xiang. Form invariance and Hojman conserved quantity for nonholonomic mechanical systems. Acta Physica Sinica, 2004, 53(8): 2413-2418. doi: 10.7498/aps.53.2413
[14]	Luo Shao-Kai, Guo Yong-Xin, Mei Feng-Xiang. Noether symmetry and Hojman conserved quantity for nonholonomic mechanical systems. Acta Physica Sinica, 2004, 53(5): 1270-1275. doi: 10.7498/aps.53.1270
[15]	Qiao Yong-Fen, Zhao Shu-Hong, Li Ren-Jie. Non Noether conserved quantity of the holonomic mechanical systems in terms of quasi-coordinates ——An extension of Hojman theorem. Acta Physica Sinica, 2004, 53(7): 2035-2039. doi: 10.7498/aps.53.2035
[16]	Luo Shao-Kai, Mei Feng-Xiang. A non-Noether conserved quantity, i.e. Hojman conserved quantity, for nonholonomic mechanical systems. Acta Physica Sinica, 2004, 53(3): 6-10. doi: 10.7498/aps.53.6
[17]	Fang Jian－Hui, Zhang Peng－Yu. The conserved quantity of Hojman for mechanicalsystems with variable mass in phase space. Acta Physica Sinica, 2004, 53(12): 4041-4044. doi: 10.7498/aps.53.4041
[18]	Xu Zhi-Xin. . Acta Physica Sinica, 2002, 51(11): 2423-2425. doi: 10.7498/aps.51.2423
[19]	FANG JIAN-HUI, ZHAO SONG-QING. LIE SYMMETRIES AND CONSERED QUANTITIES OF RELATIVISTIC ROTATIONAL VARIABLE MASS SYSTEM. Acta Physica Sinica, 2001, 50(3): 390-393. doi: 10.7498/aps.50.390
[20]	FANG JIAN-HUI. CONSERVATION LAWS OF RELATIVISTIC VARIABLE MASS SYSTEMS. Acta Physica Sinica, 2001, 50(6): 1001-1005. doi: 10.7498/aps.50.1001

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Vol. 53, Issue 12 - 2004-06-20

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Non－Noether conserved quantity of a general form for mechanical systems with variable mass

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Non－Noether conserved quantity of a general form for mechanical systems with variable mass

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