A second order gradient representation of mechanics system

Lou Zhi-Mei; Mei Feng-Xiang

doi:10.7498/aps.61.024502

Abstract

A gradient representation and a second order gradient representation of the mechanics system are studied. The differential equations of motion of the holonomic and nonholonomic mechanics systems are expressed in the canonical coordinates. A condition under which the system can be considered as a gradient system is given. A condition under which the system can be considered as a second order gradient system is obtained. Two examples are given to illustrate the application of the result.

Keywords:

Authors and contacts

Lou Zhi-Mei¹,
Mei Feng-Xiang²

1.
Department of Physics, Shaoxing University, Shaoxing 312000, China;
2.
Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China
Funds: Project supported by the National Natural Science Foundation of China (Grant No. 10932002).

References

[1]	Tarasov V E 2010 Fractional Dynamics (Beijing: Higher Education Press)
[2]	Zhou S, Fu J L, Liu Y S 2010 Chin. Phys. B 20 120301
[3]	Novoselov V S 1966 Variational Methods in Mechanics (Leningrad: L G V Press) (in Russian)
[4]	Mei F X 1985 Foundations of Mechanics of Nonholonomic systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 1985 非完整系统力学基础(北京：北京工业学院出版社)]
[5]	Mei F X 2000 Appl. Mech. Rev. 53 283
[6]	Lou Z M 2006 Chin. Phys. 15 891
[7]	Zhang H B 2002 Chin. Phys. 11 1
[8]	Zhang R C 2000 Chin. Phys. 9 561
[9]	Lou Z M 2007 Chin. Phys. 16 1182
[10]	Wang S Y, Mei F X 2002 Chin. Phys. 11 5
[11]	Wang S Y, Mei F X 2001 Chin. Phys. 10 373
[12]	Mei F X, Zheng G H 2002 Acta Mech. Sin. 18 414
[13]	Mei F X 2002 Chin. Sci. Bull. 47 2019
[14]	Mei F X, Xu X J 2005 Chin. Phys. 14 449
[15]	Xie J F, Gang T Q, Mei F X 2008 Chin. Phys. B 17 390
[16]	Sarlet W, Cantrijn F 1981 J. Phys. A: Math. Gen. 14 2227
[17]	Hojman S A1983 J. Phys. A: Math. Gen. 16 1383
[18]	Bloch A M, Krishnaprasad P S, Marsden J E, Murray R M 1996 Arch. Rational Mech. Anal. 136 21
[19]	Kara A, Mahomed F 2000 Int. J. Theor. Phys. 39 23
[20]	Beksert X, Park J H 2009 Eur. Phys. J. C 61 141
[21]	Jiang W A, Li Z J, Lou S K 2011 Chin. Phys. B 20 030202
[22]	Dong W S, Huang B X, Fang J H 2011 Chin. Phys. B 20 010204

Cited By

[1]	Tarasov V E 2010 Fractional Dynamics (Beijing: Higher Education Press)
[2]	Zhou S, Fu J L, Liu Y S 2010 Chin. Phys. B 20 120301
[3]	Novoselov V S 1966 Variational Methods in Mechanics (Leningrad: L G V Press) (in Russian)
[4]	Mei F X 1985 Foundations of Mechanics of Nonholonomic systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 1985 非完整系统力学基础(北京：北京工业学院出版社)]
[5]	Mei F X 2000 Appl. Mech. Rev. 53 283
[6]	Lou Z M 2006 Chin. Phys. 15 891
[7]	Zhang H B 2002 Chin. Phys. 11 1
[8]	Zhang R C 2000 Chin. Phys. 9 561
[9]	Lou Z M 2007 Chin. Phys. 16 1182
[10]	Wang S Y, Mei F X 2002 Chin. Phys. 11 5
[11]	Wang S Y, Mei F X 2001 Chin. Phys. 10 373
[12]	Mei F X, Zheng G H 2002 Acta Mech. Sin. 18 414
[13]	Mei F X 2002 Chin. Sci. Bull. 47 2019
[14]	Mei F X, Xu X J 2005 Chin. Phys. 14 449
[15]	Xie J F, Gang T Q, Mei F X 2008 Chin. Phys. B 17 390
[16]	Sarlet W, Cantrijn F 1981 J. Phys. A: Math. Gen. 14 2227
[17]	Hojman S A1983 J. Phys. A: Math. Gen. 16 1383
[18]	Bloch A M, Krishnaprasad P S, Marsden J E, Murray R M 1996 Arch. Rational Mech. Anal. 136 21
[19]	Kara A, Mahomed F 2000 Int. J. Theor. Phys. 39 23
[20]	Beksert X, Park J H 2009 Eur. Phys. J. C 61 141
[21]	Jiang W A, Li Z J, Lou S K 2011 Chin. Phys. B 20 030202
[22]	Dong W S, Huang B X, Fang J H 2011 Chin. Phys. B 20 010204

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Vol. 61, Issue 2 - 2012-01-20

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