Lagrange系统施加完整约束后的形式不变性

Form Invariance of Lagrange System Forced by Holonomic Constraints

研究Lagrange系统在施加完整约束后的形式不变性和守恒量.用Lagrange方程和理想双面完整约束方程在无限小变换下的形式不变性,得到Lagrange系统在施加完整约束后的形式不变性的定义和判据.指出Lagrange系统在施加完整约束后的形式不变性通常会改变.并给出一个条件,在此条件下施加完整约束后形式不变性和相应的Noether守恒量可以保持.举例说明了结果的应用.

Deals with the form invariance and the conserved quantities of a Lagrange system forced by holonomic constraints. It obtains the definition and the criterion for the form invariance of the system relying on the fact that the form of Lagrange equations and that of constrained equations with ideal bilateral holonomic constraints preserve an invariance under the infinitesimal transformations. In this case, it is shown that the form invariance of the system usually changes, and the condition under which the form invariance and the corresponding Noether conserved quantity hold is given. Two examples are finally given to illustrate the application of the results.