Generalized gradient representation of holonomic mechanical systems

Ge Wei-Kuan; Xue Yun; Lou Zhi-Mei

doi:10.7498/aps.63.110202

Abstract

A gradient system is generalized to a system in which the time appears in the potential function, and the system is called generalized gradient system. The condition under which a holonomic mechanical system can be considered as a generalized gradient system is given. If the potential function of the system can be considered as a Lyapunov function, then the Lyapunov theorems can be used to study the stability of the system.

Keywords:

Authors and contacts

1.
Department of Physics, Huzhou Teachers College, Huzhou 313000, China;
2.
School of Mechanical and Automation Engineering, Shanghai Institute of Technology, Shanghai 200235, China;
3.
Department of Physics, Shaoxing University, Shaoxing 312000, China
Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 10272050, 11372195).

References

[1]	Hirsch M W, Smale S, Devaney R L 2008 Differential Equations, Dynamical Systems and an Introduction to Chaos (Singapore: Elsevier) p165
[2]	Lou ZM, Mei F X 2012 Acta Phys. Sin. 61 024502 (in Chinese) [楼智美, 梅凤翔 2012 物理学报 61 024502]
[3]	Mei F X 2012 Mechanics in Engineering 34 89 (in Chinese) [梅凤翔 2012 力学与实践 34 89]
[4]	Mei F X, Wu H B 2012 J. Dynamics and Control 10 289 (in Chinese) [梅凤翔, 吴惠彬 2012 动力学与控制学报 10 289]
[5]	Mei F X, Cui J C, Wu H B 2012 J. of Beijing Institute of Technology 32 1288 (in Chinese) [梅凤翔, 崔金超, 吴惠彬 2012 北京理工大学学报 32 1288]
[6]	Mei F X, Wu H B 2013 Science in China Phys. Mech. Aatro. 43 538 (in Chinese) [梅凤翔, 吴惠彬 2013 中国科学物理力学天文学 43 538]
[7]	Mei F X, Wu H B 2013 Acta Phys. Sin. 62 214501 (in Chinese) [梅凤翔, 吴惠彬 2013 物理学报 62 214501]

Cited By

[1]	Hirsch M W, Smale S, Devaney R L 2008 Differential Equations, Dynamical Systems and an Introduction to Chaos (Singapore: Elsevier) p165
[2]	Lou ZM, Mei F X 2012 Acta Phys. Sin. 61 024502 (in Chinese) [楼智美, 梅凤翔 2012 物理学报 61 024502]
[3]	Mei F X 2012 Mechanics in Engineering 34 89 (in Chinese) [梅凤翔 2012 力学与实践 34 89]
[4]	Mei F X, Wu H B 2012 J. Dynamics and Control 10 289 (in Chinese) [梅凤翔, 吴惠彬 2012 动力学与控制学报 10 289]
[5]	Mei F X, Cui J C, Wu H B 2012 J. of Beijing Institute of Technology 32 1288 (in Chinese) [梅凤翔, 崔金超, 吴惠彬 2012 北京理工大学学报 32 1288]
[6]	Mei F X, Wu H B 2013 Science in China Phys. Mech. Aatro. 43 538 (in Chinese) [梅凤翔, 吴惠彬 2013 中国科学物理力学天文学 43 538]
[7]	Mei F X, Wu H B 2013 Acta Phys. Sin. 62 214501 (in Chinese) [梅凤翔, 吴惠彬 2013 物理学报 62 214501]

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Vol. 63, Issue 11 - 2014-06-05

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