中国物理B ›› 2007, Vol. 16 ›› Issue (9): 2665-2670.doi: 10.1088/1009-1963/16/9/029

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Lie symmetry algebra of one-dimensional nonconservative dynamical systems

吴润衡1, 刘翠梅2, 傅景礼3   

  1. (1)Department of Mathematics, Beijing Industrial University, Beijing 100080, China; (2)Department of Physics, Shangqiu Teachers College, Shangqiu 476000, China; (3)Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China;Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • 收稿日期:2007-01-13 修回日期:2007-03-12 出版日期:2007-09-20 发布日期:2007-09-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10672143) and the Natural Science Foundation of Henan Province, China (Grant Nos 0511022200 and 072300440220).

Lie symmetry algebra of one-dimensional nonconservative dynamical systems

Liu Cui-Mei(刘翠梅)b), Wu Run-Heng(吴润衡)c), and Fu Jing-Li(傅景礼)a)d)†   

  1. a Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; b Department of Physics, Shangqiu Teachers College, Shangqiu 476000, China; c Department of Mathematics, Beijing Industrial University, Beijing 100080, Chinad Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • Received:2007-01-13 Revised:2007-03-12 Online:2007-09-20 Published:2007-09-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10672143) and the Natural Science Foundation of Henan Province, China (Grant Nos 0511022200 and 072300440220).

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摘要： Lie symmetry algebra of linear nonconservative dynamical systems is studied in this paper. By using 1--1 mapping, the Lie point and Lie contact symmetry algebras are obtained from two independent solutions of the one-dimensional linear equations of motion.

关键词: Lie algebra, symmetry, infinitesimal transformation, nonconserved dynamical system

Abstract: Lie symmetry algebra of linear nonconservative dynamical systems is studied in this paper. By using 1--1 mapping, the Lie point and Lie contact symmetry algebras are obtained from two independent solutions of the one-dimensional linear equations of motion.

Key words: Lie algebra, symmetry, infinitesimal transformation, nonconserved dynamical system

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
02.10.Ud (Linear algebra) 02.30.Hq (Ordinary differential equations)