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A necessary and sufficient condition for transforming autonomous systems into linear autonomous Birkhoffian systems |
| Cui Jin-Chao (崔金超)a, Liu Shi-Xing (刘世兴)b, Song Duan (宋端)c |
a School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China;
b College of Physics, Liaoning University, Shenyang 110036, China;
c Physics of Medical Imaging Department, Eastern Liaoning University, Dandong 118001, China |
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Abstract The problem of transforming autonomous systems into Birkhoffian systems is studied. A reasonable form of linear autonomous Birkhoff equations is given. By combining them with the undetermined tensor method, a necessary and sufficient condition for an autonomous system to have a representation in terms of linear autonomous Birkhoff equations is obtained. The methods of constructing Birkhoffian dynamical functions are given. Two examples are given to illustrate the application of the results.
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Received: 21 January 2013
Revised: 24 May 2013
Accepted manuscript online:
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PACS:
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45.05.+x
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(General theory of classical mechanics of discrete systems)
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02.30.Zz
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(Inverse problems)
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45.10.-b
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(Computational methods in classical mechanics)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10932002, 11172120, and 11202090). |
Corresponding Authors:
Song Duan
E-mail: songduan620606@163.com
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Cite this article:
Cui Jin-Chao (崔金超), Liu Shi-Xing (刘世兴), Song Duan (宋端) A necessary and sufficient condition for transforming autonomous systems into linear autonomous Birkhoffian systems 2013 Chin. Phys. B 22 104501
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