Conformal invariance and conserved quantity of Lagrange systems under Lie point transformation

Conformal invariance and conserved quantities of Lagrange system under Lie point transformation are studied. Firstly, the definition of conformal invariance and determining equation for the Lagrange system are provided. Secondly, the relationship between the system's conformal invariance and Lie symmetry are discussed; the necessary and sufficient condition on which the system s conformal invariance would be Lie symmetry under the infinitesimal one-parameter point transformation group is deduced; and the conserved quantities of the system are given. Lastly, an illustration example is introduced.