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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 |
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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.
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Received: 13 February 2016
Revised: 23 May 2016
Accepted manuscript online:
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PACS:
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02.30.Jr
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(Partial differential equations)
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45.20.Jj
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(Lagrangian and Hamiltonian mechanics)
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11.30.-j
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(Symmetry and conservation laws)
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| 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
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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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