约束力学系统的Noether对称性

Noether Symmetries of Constrained Mechanical Systems

利用变分法研究非完整约束力学系统的Ｎｏｅｔｈｅｒ对称性问题，结果表明，如果非完整力学系统的动力学性质和约束的几何性质满足某种条件，那么该系统的对称性与守恒量之间也存在着对应关系．

According to the classical Noether's theorem, there exist intrinsic corresponding relations between the symmetries of general mechanical systems and conserved quantities. If mechanical systems are subject to nonholonomic constraints, the phase spaces of the systems are no longer of symplectic structures and the internal symmetries are broken. In this paper Noether symmetries of nonholonomic constrained mechanical systems are studied by means of calculus of variations. The results indicate that there also exist corresponding relations between symmetries and conserved quantities of the nonholonomic constrained mechanical systems, if the dynamical properties of the systems and geometrical structure of the constraints satisfy some requirements.