A new type of conserved quantity of Mei symmetry for Lagrange system

This paper studies a new type of conserved quantity which is directlyinduced by Mei symmetry of the Lagrange system. Firstly, thedefinition and criterion of Mei symmetry for the Lagrange system aregiven. Secondly, a coordination function is introduced, and theconditions of existence of the new conserved quantity as well as itsforms are proposed. Lastly, an illustrated example is given. Theresult indicates that the coordination function can be selectedproperly according to the demand for finding the gauge function, andthereby the gauge function can be found more easily. Furthermore,since the choice of the coordination function has multiformity, manymore conserved quantities of Mei symmetry for the Lagrange systemcan be obtained.