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Chin. Phys. B, 2016, Vol. 25(10): 100201    DOI: 10.1088/1674-1056/25/10/100201
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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 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
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.
Keywords:  gradient system      combined gradient system      mechanical system      stability  
Received:  13 February 2016      Revised:  23 May 2016      Published:  05 October 2016
PACS:  02.30.Jr (Partial differential equations)  
  45.20.Jj (Lagrangian and Hamiltonian mechanics)  
  11.30.-j (Symmetry and conservation laws)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11372169 and 11272050).
Corresponding Authors:  Xiang-Wei Chen     E-mail:  hnchenxw@163.com

Cite this article: 

Xiang-Wei Chen(陈向炜), Ye Zhang(张晔), Feng-Xiang Mei(梅凤翔) An application of a combined gradient system to stabilize a mechanical system 2016 Chin. Phys. B 25 100201

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