非完整非保守力学系统在相空间的Lie对称性与守恒量

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基金项目: 国家自然科学基金资助项目(19572018)

Lie Symmetries and Conserved Quantities of Nonconservative Nonholonomic Systems in Phase Space

摘要: 在相空间引入无限小变换,研究非完整非保守力学系统运动微分方程的不变性和守恒量。建立Lie对称确定方程,得到Lie对称的结构方程和守恒量形式,并举例说明结果的应用。
- 非完整约束 /
- 相空间 /
- Lie对称
Abstract: The invariance and conserved quantities of the nonconservative nonholonomic systems are studied by introducing the infinitesimal transformations in phase space. The Lie's symmetrical determining equations are established. The Lie's symmetrical structure equation is obtained. An example to illustrate the application of the result is given.
- nonholonomic constraint /
- phase space /
- Lie’s symmetry

[1]	Noether A E. Invariante variations probleme[J].Gttinger Nachrichten, Mathematisch-Physicalishe Klasse,1918,2:235～257.
[2]	梅风翔,刘端,罗勇.高等分析力学[M].北京:北京理工大学出版社,1991.
[3]	李子平,经典和量子约束系统及其对称性质[M].北京:北京工业大学出版社,1993.
[4]	Liu Duan. Noether's theorem and its inverse of nonholonomic nonconservative dynamical systems[J].Science in China (Series A),1990,34(4):419～429.
[5]	Lutzky M. Dynamical symmetries and conserved quantities[J].J Phy A, Math Gen,1979,12(7):973～981.
[6]	Bluman G W, Kumei S. Symmetries and Differential Equations[M].New York: Springer-Verlag,1989.
[7]	赵跃宇,非保守力学系统的Lie对称性和守恒量[J].力学学报,1994,26(3):380～384.
[8]	Santilli R M. Foundations of Theoretical Mechanics Ⅱ[M].New York: Springer-Verlag,1983.