期刊：
JOURNAL OF MECHANICS,2015年31(5):515-523 ISSN：1727-7191
通讯作者：
Cai, J. -L.
作者机构：
[Huang, W. -L.] Hunan City Univ, Dept Phys & Telecom Engn, Yiyang, Peoples R China.;[Cai, J. -L.] Hangzhou Normal Univ, Coll Sci, Hangzhou, Zhejiang, Peoples R China.
通讯机构：
[Cai, J. -L.] H;Hangzhou Normal Univ, Coll Sci, Hangzhou, Zhejiang, Peoples R China.
关键词：
Non-holonomic system;Variable mass;Mei symmetry;Inverse problem
摘要：
The inverse problem of the Mei symmetry for nonholonomic systems with variable mass is studied. Firstly, the authors discuss the Mei symmetry of the holonomic system opposite to a nonholonomic system. Secondly, weak and strong Mei symmetries of a nonholonomic system are concluded through restriction equations and additional restriction equations. Thirdly, the relevant conserved quantity is deduced by means of the structure equation for the gauge function. Fourthly, the inverse problem of the Mei symmetry is obtained by the Noether symmetry. Finally, the paper offers an example to illustrate the application of the research result.
作者机构：
[Cai Jian-Le; Huang Wei-Li] Hangzhou Normal Univ, Coll Sci, Hangzhou 310018, Zhejiang, Peoples R China.;[Huang Wei-Li] Hunan City Univ, Dept Phys & Telecom Engn, Yiyang 413000, Peoples R China.
通讯机构：
[Cai Jian-Le] H;Hangzhou Normal Univ, Coll Sci, Hangzhou 310018, Zhejiang, Peoples R China.
关键词：
Higher-Order Lagrange Systems;Lie Point Transformation
摘要：
Conformal invariance and conserved quantities for a higher-order Lagrange system by Lie point transformation of groups are studied. The differential equation of motion for the higher-order Lagrange system is introduced. The definition of conformal invariance for the system together with its determining equations and conformal factor are provided. The necessary and sufficient condition that the system's conformal invariance would be Lie symmetry by the infinitesimal one-parameter point transformation group is deduced. The conserved quantity of the system is derived using the structural equation satisfied by the gauge function. An example of a higher-order mechanical system is offered to illustrate the application of the result.
