A new type of conserved quantity induced by symmetries of Lagrange system

This Letter investigates a new type of conserved quantity induced by symmetries of Lagrange system. Firstly, the new type of conserved quantity which is directly induced by Lie symmetry of Lagrange system is obtained. The condition of existence of the new conserved quantity as well as its form is given. Secondly, the connections between Noether, Mei and Lie symmetry are discussed, and this new type of conserved quantity can also be induced by Noether and Mei symmetry of the system. Finally, an example is discussed to illustrate these results.