Conformal invariance and conserved quantities for a nonholonomic system of Chetaev’s type with variable mass are studied. The conformal factor expressions are derived. The necessary and sufficient conditions are obtained to make the system’s conformal invariance Lie symmetrical. The conformal invariance of the weak and strong Lie symmetries for the system is given. The corresponding conserved quantities of the system are derived. Finally, an application of the result is shown with an example.
[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.
[Cai Jian-Le] Hangzhou Normal Univ, Coll Sci, Hangzhou 310018, Zhejiang, Peoples R China.
Higher-Order Lagrange Systems;Lie Point Transformation
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.
[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.
[Cai, J. -L.] Hangzhou Normal Univ, Coll Sci, Hangzhou, Zhejiang, Peoples R China.
Inverse problem;Mei symmetry;Non-holonomic system;Variable mass
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.