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A Condition of Transforming General Dynamical Systems into Linear Birkhoffian Dynamical Systems

ZHANG Xingwu, HUANG Kefu, LIU Kaixin   

  1. Department of Mechanics and Engineering Science, Peking University, Beijing, 100871
  • Received:2002-05-25 Online:2003-05-20 Published:2003-05-20


张兴武, 黄克服, 刘凯欣   

  1. 北京大学力学与工程科学系,北京,100871

Abstract: A condition of transforming general linear dynamical systems into linear Birkhoffian dynamical systems is studied. The condition and the procedure of transformation is given and proved. A theorem of the equivalence between linear Birkhoffian systems and linear Hamiltonian systems is given. According to the condition given by using the Jordan form, the non-degenerate condition of the Birkhoff tensor is analyzed from several aspects.

Key words: linear dynamical systems, Birkhoffian equations, Hamiltonian equations, Jordan form

摘要: 研究一般线性动力系统何时转化为线性自治Birkhoff动力系统的问题,给出线性自治Birkhoff动力系统与线性自治Hamilton动力系统等价性的定理,并推导出2n维线性动力系统转化为线性自治Birkhoff动力系统条件,通过运用若当形对转化条件进行分析,分情况给出Bikhoff张量非退化的条件。

关键词: 线性动力系统, Birkhoff方程, Hamilton方程, 若当形

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