New conserved quantities of Noether--Mei symmetry of mechanical system in phase space

This paper studies two new types of conserved quantities deduced byNoether--Mei symmetry of mechanical system in phase space. Thedefinition and criterion of Noether--Mei symmetry for the system aregiven. A coordination function is introduced, and the conditionsunder which the Noether--Mei symmetry leads to the two types ofconserved quantities and the forms of the two types of conservedquantities are obtained. An illustrative example is given. Thecoordination function can be selected according to the demand forfinding the gauge function, and the choice of the coordinationfunction has multiformity, so more conserved quantities deduced fromNoether--Mei symmetry of mechanical system can be obtained.