单面非完整系统相对于非惯性系的Noether定理

NOETHER'S THEOREM OF NON HOLONOMIC SYSTEMS WITH UNILATERAL CONSTRAINTS RELATIVE TO NON-INERTIAL REFERENCE FRAME

本文研究了单面非完整系统相对于非惯性系的 Noether定理及逆定理。首先给出系统的 d′Alembert- Lagrange原理及非等时变分 ;其次基于微分变分原理在无限小变换下的不变性质 ,得到单面非完整系统相对于非惯性系的 Noether定理及逆定理 ;最后举例说明结果的应用。

Principle of d'Alembert-Lagrange for a system relative to a non-inertial reference frame and non-isochronal variation is first presented. Noether's theorem and her inverse theorem for the above system relative to a non-inertial reference frame are then studied, based upon the invariance of the differential variational principle under infinitesimal transformations. An example to illustrate the application of the result is finally given.