中国物理B ›› 2016, Vol. 25 ›› Issue (10): 100201-100201.doi: 10.1088/1674-1056/25/10/100201

• GENERAL •    下一篇

An application of a combined gradient system to stabilize a mechanical system

Xiang-Wei Chen(陈向炜), Ye Zhang(张晔), Feng-Xiang Mei(梅凤翔)   

  1. 1 Department of Physics and Information Engineering, Shangqiu Normal University, Shangqiu 476000, China;
    2 School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China;
    3 School of Aerospace, Beijing Institute of Technology, Beijing 100081, China
  • 收稿日期:2016-02-13 修回日期:2016-05-23 出版日期:2016-10-05 发布日期:2016-10-05
  • 通讯作者: Xiang-Wei Chen E-mail:hnchenxw@163.com
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11372169 and 11272050).

An application of a combined gradient system to stabilize a mechanical system

Xiang-Wei Chen(陈向炜)1, Ye Zhang(张晔)2, Feng-Xiang Mei(梅凤翔)3   

  1. 1 Department of Physics and Information Engineering, Shangqiu Normal University, Shangqiu 476000, China;
    2 School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China;
    3 School of Aerospace, Beijing Institute of Technology, Beijing 100081, China
  • Received:2016-02-13 Revised:2016-05-23 Online:2016-10-05 Published:2016-10-05
  • Contact: Xiang-Wei Chen E-mail:hnchenxw@163.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11372169 and 11272050).

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摘要： A gradient system and a skew-gradient system can be merged into a combined gradient system. The differential equations of the combined gradient system are established and its property is studied. If a mechanical system can be represented as a combined gradient system, the stability of the mechanical system can be studied by using the property of the combined gradient system. Some examples are given to illustrate the applications of the results.

关键词: gradient system, combined gradient system, mechanical system, stability

Abstract: A gradient system and a skew-gradient system can be merged into a combined gradient system. The differential equations of the combined gradient system are established and its property is studied. If a mechanical system can be represented as a combined gradient system, the stability of the mechanical system can be studied by using the property of the combined gradient system. Some examples are given to illustrate the applications of the results.

Key words: gradient system, combined gradient system, mechanical system, stability

中图分类号:  (Partial differential equations)

  • 02.30.Jr
45.20.Jj (Lagrangian and Hamiltonian mechanics) 11.30.-j (Symmetry and conservation laws)