单面非完整力学系统的Noether理论

Noether's Theory for Mechanical Systems with Unilateral Nonholonomic Constraints

研究具有单面非完整约束的力学系统的Ｎｏｅｔｈｅｒ对称性与守恒量。基于Ｈａｍｉｌｔｏｎ作用量 在ｒ参数有限变换群Ｃｒ的无限小变换下的不变性，建立了系统的广义Ｎｏｅｔｈｅｒ定理及其道定理， 并举例说明结果的应用。

In this paper the Noether symmetries and the conserved quantities for the mechanical systems with unilateral nonholonomic constraints are studied. The generalized Noether's theorem and its inverse theorem of the systems are established on the basis of the invariant properties of the Hamiltonian action with respect to the action of the infinitesimal transformation of parameter finite group of transformation and an example is given to illustrate the application of the results.