二阶单面非完整系统的Noether定理

Noether′s theorem of second order nonholonomic systems with unilateral constraints

研究二阶单面非完整系统的Noether定理及逆定理.首先给出系统的Gauss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,得到了二阶单面非完整系统的Noether定理及逆定理;最后举例说明结果的应用.

In the paper, the Noether′s theorem of second order nonholonomic systems with unilateral constraints is studied. Firstly, the Gauss principle of the system and non isochronal variation are presented. Secondly, based upon the invariance of the differential variational principle under the infinitesimal transformations of group the Noether′s theorem and the Noether′s inverse theorem are obtained for the above systems. Finally, an example to illustrate the application of the result is given.