Lie symmetries and Hojman conserved quantities of one kind of differential equations of motion of nonholonomic systems

Hu Chu-Le

doi:10.7498/aps.56.3675

Abstract
The Lie symmetries and Hojman conserved quantities of one kind of differential equations of motion of nonholonomic systems are studied. The determining equations and the restriction equations of Lie symmetries of the system are obtained. The condition under which a conserved quantity exists is established and the form of the conserved quantity is given. An example is given to illustrate the application of the result.

Keywords:
analytical mechanics /

nonholonomic system /

symmetry /

Hojman conserved quantity
Authors and contacts
Hu Chu-Le

1.
呼伦贝尔学院物理系，海拉尔 021008
References

Cited By

[1]	Cai Jian-Le, Shi Sheng-Shui. Conformal invariance and conserved quantity of Mei symmetry for the nonholonomic system of Chetaev's type. Acta Physica Sinica, 2012, 61(3): 030201. doi: 10.7498/aps.61.030201
[2]	Zhang Bin, Fang Jian-Hui, Zhang Ke-Jun. Symmetry and conserved quantity of Lagrangians for nonholonomic variable mass system. Acta Physica Sinica, 2012, 61(2): 021101. doi: 10.7498/aps.61.021101
[3]	Yang Xin-Fang, Sun Xian-Ting, Wang Xiao-Xiao, Zhang Mei-Ling, Jia Li-Qun. Mei symmetry and Mei conserved quantity of Appell equations for nonholonomic systems of Chetaevs type with variable mass. Acta Physica Sinica, 2011, 60(11): 111101. doi: 10.7498/aps.60.111101
[4]	Lou Zhi-Mei. The extended Prelle-Singer method for the conserved quantities of second-ordinary nonlinear coupled dynamics systems and their symmetries. Acta Physica Sinica, 2010, 59(2): 719-723. doi: 10.7498/aps.59.719
[5]	Zhang Yi, Xue Yun, Ge Wei-Kuan. Symmetries and conserved quantities of the Rosenberg problem. Acta Physica Sinica, 2010, 59(7): 4434-4436. doi: 10.7498/aps.59.4434
[6]	Jia Li-Qun, Luo Shao-Kai, Zhang Yao-Yu. Mei symmetry and Mei conserved quantity of Nielsen equation for a nonholonomic system. Acta Physica Sinica, 2008, 57(4): 2006-2010. doi: 10.7498/aps.57.2006
[7]	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
[8]	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
[9]	Zheng Shi-Wang, Jia Li-Qun. Mei symmetry and conserved quantity of Tzénoff equations for nonholonomic systems. Acta Physica Sinica, 2007, 56(2): 661-665. doi: 10.7498/aps.56.661
[10]	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
[11]	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
[12]	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
[13]	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
[14]	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
[15]	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
[16]	Zhang Yi. Effects of non-conservative forces and nonholonomic constraints on Lie symmetrie s of a Hamiltonian system. Acta Physica Sinica, 2003, 52(6): 1326-1331. doi: 10.7498/aps.52.1326
[17]	Zhang Yi. . Acta Physica Sinica, 2002, 51(8): 1666-1670. doi: 10.7498/aps.51.1666
[18]	Zhang Yi. . Acta Physica Sinica, 2002, 51(3): 461-464. doi: 10.7498/aps.51.461
[19]	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
[20]	MEI FENG-XIANG. LIE SYMMETRIES AND CONSERVED QUANTITIES OF NONHOLONOMIC SYSTEMS WITH SERVOCONSTR AINTS. Acta Physica Sinica, 2000, 49(7): 1207-1210. doi: 10.7498/aps.49.1207

Catalog

Vol. 56, Issue 7 - 2007-04-05

Metrics

Abstract views: 7542
PDF Downloads: 812
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板

Lie symmetries and Hojman conserved quantities of one kind of differential equations of motion of nonholonomic systems

Abstract

Authors and contacts

References

Cited By

Catalog

Metrics

Authors

Referees

About Journal

About

Search

Article

留言板

Lie symmetries and Hojman conserved quantities of one kind of differential equations of motion of nonholonomic systems

Abstract

Authors and contacts

References

Cited By

Catalog

Metrics

Publishing process

Authors

Referees

About Journal

About