Conformal invariance, Noether symmetry and Lie symmetry for holonomic mechanical system with variable mass

Abstract

The conformal invariance of holonomic mechanical system with variable mass is studied. Firstly, the definition of conformal invariance for holonomic mechanical system with variable mass is given; secondly, the relation between the conformal invariance and the Noether symmetry is discussed, and the Noether conserved quantity led by the conformal invariance is obtained; finally, the relation between the conformal invariance and the Lie symmetry is discussed, and the Hojman conserved quantity caused by the conformal invariance of the systems is obtained. In the paper, an example is given to illustrate the application of the results.