完整力学系统的广义梯度表示

葛伟宽; 薛纭; 楼智美

doi:10.7498/aps.63.110202

摘要

将梯度系统推广到包含时间的情形，称之为广义梯度系统. 给出完整力学成为梯度系统的条件. 如果广义梯度系统的势函数可以成为Lyapunov函数，那么可用Lyapunov定理来研究系统的稳定性.

关键词:

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:

作者及机构信息

1.
湖州师范学院物理系, 湖州 313000;

2.
上海应用技术学院机械与自动化工程学院, 上海 200235;

3.
绍兴文理学院物理系, 绍兴 312000

基金项目: 国家自然科学基金（批准号：11272050，11372195）资助的课题.

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).

参考文献

[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]

施引文献

[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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