Conformal invariance and conserved quantities of Mei symmetry for general holonomic systems

Abstract

Conformal invariance and conserved quantities of Mei symmetry for general holonomic systems are studied thoroughly. By introducing a single-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators, definitions of the conformal invariance of Mei symmetry for the system are provided. Conditions that the conformal invariance should satisfy are derived using the Euler operator, and their determining equations are then presented. Moreover, the relationship between conformal invariance and the three symmetries, i.e., Noether symmetry, Lie symmetry and Mei symmetry, are discussed. The system’s corresponding conserved quantities are obtained, according to the structure equation satisfied by the gauge function. Finally, an example is provided to illustrate how the given result can be applied.