The Lie symmetries and the conserved quantities of the second-order nonholonomic mechanical system are studied. Firstly, by using the invariance of the differential equation of motion under the infinitesimal tran, for...The Lie symmetries and the conserved quantities of the second-order nonholonomic mechanical system are studied. Firstly, by using the invariance of the differential equation of motion under the infinitesimal tran, formations, the determining equations and the restriction equations of the Lie symmetries of the system are established, and the structure equation and the conservative quantities of the Lie symmetries are obtained. Secondly, the inverse problems of the Lie symmetries are studied. Finally, an example is given to illustrate the application of the result.展开更多
The conservation law of nonholonomic system of second-order non-Chataev's type in event space is studied The Jourdain's principle in event space is presented. The invariant condition of the Jourdain's prin...The conservation law of nonholonomic system of second-order non-Chataev's type in event space is studied The Jourdain's principle in event space is presented. The invariant condition of the Jourdain's principle under infinitesimal transformation is given by introducing Jourdain's generators in event space. Then the conservation law of the system in event space is obtained under certain conditions. Finally a calculating example is given.展开更多
文摘The Lie symmetries and the conserved quantities of the second-order nonholonomic mechanical system are studied. Firstly, by using the invariance of the differential equation of motion under the infinitesimal tran, formations, the determining equations and the restriction equations of the Lie symmetries of the system are established, and the structure equation and the conservative quantities of the Lie symmetries are obtained. Secondly, the inverse problems of the Lie symmetries are studied. Finally, an example is given to illustrate the application of the result.
文摘The conservation law of nonholonomic system of second-order non-Chataev's type in event space is studied The Jourdain's principle in event space is presented. The invariant condition of the Jourdain's principle under infinitesimal transformation is given by introducing Jourdain's generators in event space. Then the conservation law of the system in event space is obtained under certain conditions. Finally a calculating example is given.
