Special Lie symmetry and Hojman conserved quantity of Appell equations in a dynamical system of relative motion

doi:10.1088/1674-1056/20/1/010203

Abstract Special Lie symmetry and the Hojman conserved quantity for Appell equations in a dynamical system of relative motion are investigated. The definition and the criterion of the special Lie symmetry of Appell equations in a dynamical system of relative motion under infinitesimal group transformation are presented. The expression of the equation for the special Lie symmetry of Appell equations and the Hojman conserved quantity, deduced directly from the special Lie symmetry in a dynamical system of relative motion, are obtained. An example is given to illustrate the application of the results.

Keywords: dynamics of relative motion Appell equations special Lie symmetry Hojman conserved quantity

Received: 19 June 2010
Revised: 29 June 2010
Accepted manuscript online:

PACS:	02.20.Sv	(Lie algebras of Lie groups)
	11.30.-j	(Symmetry and conservation laws)

Cite this article:

Xie Yin-Li(解银丽), Jia Li-Qun(贾利群), and Luo Shao-Kai(罗绍凯) Special Lie symmetry and Hojman conserved quantity of Appell equations in a dynamical system of relative motion 2011 Chin. Phys. B 20 010203

[1]	Bargmann V 1954 On Unitary Ray Representation of Continuous Groups. Ann. Math. 59 1
[2]	Maeda S 1980 Math. Japonica. 23 231
[3]	Haidari A D 1986 J. Math. Phys. 27 2409
[4]	Hojman S A 1992 J. Phys. A: Math. Gen. 25 1291
[5]	Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) (in Chinese)
[6]	Chen X W and Mei F X 2000 Chin. Phys. 9 721
[7]	Robert M L and Matthew P 2001 J. Geom. Phys. 39 276
[8]	Zhang Y 2003 Acta Phys. Sin. 52 1832 (in Chinese)
[9]	Mei F X 2004 Symmetries and Conserved Quantities of Constranined Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese)
[10]	Fu J L, Chen L Q and Xie F P 2004 Chin. Phys. 13 1611
[11]	Ge W K and Zhang Y 2005 Acta Phys. Sin. 54 4985 (in Chinese)
[12]	Lall S and West M 2006 J. Phys. A: Math. Gen. 39 5509
[13]	Jalnapurkar S M, Leok M, Marsden J E and West M 2006 J. Phys. A: Math. Gen. 39 5521
[14]	Zhang Y 2008 Acta Phys. Sin. 57 2643 (in Chinese)
[15]	Fang J H 2009 Acta Phys. Sin. 58 3617 (in Chinese)
[16]	Mei F X 1988 Analytical Mechanics Topics (Beijing: Beijing Institute of Technology Press) p22 (in Chinese)
[17]	Mei F X, Liu D and Luo Y 1991 Advanced Analytical Mechanics (Beijing: Beijing Institute of Technology Press) (in Chinese)
[18]	Mei F X 2001 Chin. Phys. 10 177
[19]	Li R J, QiaoY F and Meng J 2002 Acta Phys. Sin. 51 1 (in Chinese)
[20]	Luo S K 2002 Acta Phys. Sin. 51 712 (in Chinese)
[21]	Jia L Q, Zhang Y Y and Zheng S W 2007 J. Yunnan Univ. 29 589 (in Chinese)
[22]	Jia L Q, Xie J F and Zheng S W 2008 Chin. Phys. B 17 17
[23]	Luo S K, Zhang Y F 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science Press) (in Chinese)
[24]	Jia L Q, Cui J C, Luo S K and Yang X F 2009 Chin. Phys. Lett. 26 030303
[25]	Cui J C, Jia L Q and Yang X F 2009 J. Henan Norm. Univ. (Natural Science) 37 (refeq2) 70 (in Chinese)
[26]	Li Y C, Xia L L, Wang X M and Liu X W 2010 Acta Phys. Sin. 59 3639 (in Chinese)

[1]	Lie symmetry and its generation of conserved quantity of Appell equation in a dynamical system of the relative motion with Chetaev-type nonholonomic constraints Wang Xiao-Xiao (王肖肖), Han Yue-Lin (韩月林), Zhang Mei-Ling (张美玲), Jia Li-Qun (贾利群). Chin. Phys. B, 2013, 22(2): 020201.
[2]	Form invariance and approximate conserved quantity of Appell equations for a weakly nonholonomic system Jia Li-Qun(贾利群), Zhang Mei-Ling(张美玲), Wang Xiao-Xiao(王肖肖), and Han Yue-Lin(韩月林) . Chin. Phys. B, 2012, 21(7): 070204.
[3]	Mei symmetry and Mei conserved quantity of the Appell equation in a dynamical system of relative motion with non-Chetaev nonholonomic constraints Wang Xiao-Xiao(王肖肖), Sun Xian-Ting(孙现亭), Zhang Mei-Ling(张美玲), Han Yue-Lin(韩月林), and Jia Li-Qun(贾利群) . Chin. Phys. B, 2012, 21(5): 050201.
[4]	Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion Zhang Mei-Ling (张美玲), Wang Xiao-Xiao (王肖肖), Han Yue-Lin (韩月林), Jia Li-Qun (贾利群). Chin. Phys. B, 2012, 21(10): 100203.
[5]	Conformal invariance and a kind of Hojman conserved quantity of the Nambu system Li Yan(李燕),Fang Jian-Hui(方建会),and Zhang Ke-Jun(张克军). Chin. Phys. B, 2011, 20(3): 030201.
[6]	Poisson theory and integration method for a dynamical system of relative motion Zhang Yi(张毅) and Shang Mei(尚玫) . Chin. Phys. B, 2011, 20(2): 024501.
[7]	Lie symmetry and Hojman conserved quantity of a Nielsen equation in a dynamical system of relative motion with Chetaev-type nonholonomic constraint Wang Xiao-Xiao(王肖肖), Sun Xian-Ting(孙现亭), Zhang Mei-Ling(张美玲), Xie Yin-Li(解银丽), and Jia Li-Qun(贾利群) . Chin. Phys. B, 2011, 20(12): 124501.
[8]	Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion Zhang Mei-Ling(张美玲), Sun Xian-Ting(孙现亭), Wang Xiao-Xiao(王肖肖), Xie Yin-Li(解银丽), and Jia Li-Qun(贾利群) . Chin. Phys. B, 2011, 20(11): 110202.
[9]	Hojman conserved quantity deduced by weak Noether symmetry for Lagrange systems Xie Jia-Fang(解加芳), Gang Tie-Qiang(冮铁强), and Mei Feng-Xiang(梅凤翔). Chin. Phys. B, 2008, 17(2): 390-393.
[10]	Lie symmetry and Hojman conserved quantity of Nambu system Lin Peng (蔺鹏), Fang Jian-Hui (方建会), Pang Ting (庞婷). Chin. Phys. B, 2008, 17(12): 4361-4364.
[11]	Mei symmetry and generalized Hojman conserved quantity for variable mass systems with unilateral holonomic constraints Jing Hong-Xing(荆宏星), Li Yuan-Cheng(李元成), Wang Jing(王静), Xia Li-Li(夏丽莉), and Hou Qi-Bao(后其宝). Chin. Phys. B, 2007, 16(7): 1827-1831.
[12]	Hojman conserved quantity for nonholonomic systems of unilateral non-Chetaev type in the event space Jia Li-Qun(贾利群), Zhang Yao-Yu(张耀宇), and Luo Shao-Kai(罗绍凯). Chin. Phys. B, 2007, 16(11): 3168-3175.
[13]	Three-order form invariance and conserved quantity Yang Xue-Hui(杨学慧) and Ma Shan-Jun(马善钧). Chin. Phys. B, 2006, 15(8): 1672-1677.
[14]	FORM INVARIANCE OF APPELL EQUATIONS Mei Feng-xiang (梅凤翔). Chin. Phys. B, 2001, 10(3): 177-180.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Special Lie symmetry and Hojman conserved quantity of Appell equations in a dynamical system of relative motion

Cite this article:

Online attention