ADVANCES IN THE SYMMETRIES AND CONSERVED QUANTITIES OF CLASSICAL CONSTRAINED SYSTEMS
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摘要: 介绍有关经典约束力学系统对称性与守恒量研究的近代发展.提出经典力学发展的5个阶段以及待研究的3个问题. 介绍Noether对称性,Lie对称性, 形式不变性, Lagrange对称性,共形不变性以及由它们导致的守恒量, 并提出若干问题.
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关键词:
- 经典力学, 对称性, 守恒量,积分
Abstract: This paper summarizedthe recent progress in the symmetries and conserved quantities ofclassical constrained mechanical systems. The five stages ofclassical mechanics are introduced and the three problems areproposed. The Noether symmetry, the Lie symmetry, the forminvariance, the symmetry of Lagrangians, the conformal invarianceand the conserved quantities of the systems are dsicussed, andsome future research problems are proposed. -
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