经典约束力学系统对称性与守恒量研究进展

ADVANCES IN THE SYMMETRIES AND CONSERVED QUANTITIES OF CLASSICAL CONSTRAINED SYSTEMS

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.

This paper summarized the recent progress in the symmetries and conserved quantities of classical constrained mechanical systems. The five stages of classical mechanics are introduced and the three problems are proposed. The Noether symmetry, the Lie symmetry, the form invariance, the symmetry of Lagrangians, the conformal invariance and the conserved quantities of the systems are dsicussed, and some future research problems are proposed.