A necessary and sufficient condition for transforming autonomous systems into linear autonomous Birkhoffian systems

doi:10.1088/1674-1056/22/10/104501

中国物理B ›› 2013, Vol. 22 ›› Issue (10): 104501-104501.doi: 10.1088/1674-1056/22/10/104501

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

A necessary and sufficient condition for transforming autonomous systems into linear autonomous Birkhoffian systems

崔金超^a, 刘世兴^b, 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

收稿日期:2013-01-21 修回日期:2013-05-24 出版日期:2013-08-30 发布日期:2013-08-30
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10932002, 11172120, and 11202090).

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

Received:2013-01-21 Revised:2013-05-24 Online:2013-08-30 Published:2013-08-30
Contact: Song Duan E-mail:songduan620606@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10932002, 11172120, and 11202090).

摘要/Abstract

摘要： 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.

关键词: autonomous systems, linear autonomous Birkhoff’, s equations, non-Hamiltonian systems, Whittaker’, s equations

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.

Key words: autonomous systems, linear autonomous Birkhoff’, s equations, non-Hamiltonian systems, Whittaker’, s equations

中图分类号: (General theory of classical mechanics of discrete systems)

45.05.+x

02.30.Zz (Inverse problems) 45.10.-b (Computational methods in classical mechanics)

崔金超, 刘世兴, 宋端. A necessary and sufficient condition for transforming autonomous systems into linear autonomous Birkhoffian systems[J]. 中国物理B, 2013, 22(10): 104501-104501.

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[J]. Chin. Phys. B, 2013, 22(10): 104501-104501.

参考文献 19

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A necessary and sufficient condition for transforming autonomous systems into linear autonomous Birkhoffian systems

A necessary and sufficient condition for transforming autonomous systems into linear autonomous Birkhoffian systems

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