Symmetries And Conserved Quantities Of Nonholonomic Singular Mechanical Systems In Terms Of Quasi-coordinat

Dynamics study of the symmetry and conserved quantity in analytical mechanics has an important and popular significance.At present,the research on the dynamic system of conservation,the most method widely used is the symmetry theory.According the symmetry theory,the main methods to find conserved quantities are the followings: Noether symmetry,Lie symmetry,form invariance(Mei symmetry)and conformal invariance theories.In the paper,we study the symmetries and conserved quantities of nonholonomic singular mechanical systems in terms of quasi-coordinates.We establish the differential equations of systems.Noether symmetry,Lie symmetry,form invariance(Mei symmetry)and conformal invariance of nonholonomic singular mechanical systems in terms of quasi-coordinates are studied.Firstly,we give the Noether equation and the form of Noether conserved quantity of Noether symmetry;Secondly,the Lie symmetry definition and criterion and the conservation of the expression from the nonholomic singular mechanical systems in terms of quasi-coordinates are given,and then we study the Lie symmetry and conserved quantity inverse problem of the nonholonomic singular mechanical systems in terms of quasi-coordinates.Besides,we give the Mei symmetry definition and criterion and the conservation of the expression fromthe nonholonomic singular mechanical systems in terms of quasicoordinates,and then the inverse problem of Mei symmetry and conserved quantity of the nonholonomic singular mechanical systems in terms of quasi-coordinates is studied.Finally,we simply study the conformal invariance of the nonholonomic singular mechanical systems in terms of quasi-coordinates and discuss the relationship among the conformal invariance,Noether symmetry and Lie symmetry.We also have the corresponding criterion equations and the conservations of the expression.Meanwhile,the paper gives examples to illustrate the application of the result.