Conformal invariance and conserved quantity of Mei symmetry for higher-order nonholonomic system

Abstract

The conformal invariance and conserved quantity of Mei symmetry for a higher-order nonholonomic mechanical system are presented. Introducing an infinitesimal transformation group and infinitesimal generator vector, the definition of conformal invariance of Mei symmetry and the determining equation for the holonomic system which corresponds to a higher-order nonholonomic system are provided, and the relationship between Mei symmetry and conformal invariance of the system is discussed. The basis of restriction equations and additional restriction equations, the conformal invariance of weak and strong Mei symmetry for the higher-order nonholonomic mechanical system is constructed. With the aid of a structure equation that the gauge function satisfies, the system’s corresponding conserved quantity is derived. Finally, an example is given to illustrate the application of the method and its result.