Lie Symmetry And Conserved Quantities Of Singular Systems On Time Scales

Singular systems exist widely in mathematics and physics.Therefore,the study of singular systems plays an important role in promoting the development of modern mathematics and physics.In this paper,Lie symmetry theory of singular systems on time scales is studied.The lie symmetry theory for a singular non-conservative Lagrangian system,a singular system with nonholonomic constrains of Chetaev's type,Hamilton canonical equations in a singular system are discussed.Research on the lie symmetry of a singular non-conservative Lagrangian system on time scales.Considering the system is subjected to non-conservative forces,the differential equations of motion of the system are deduced.Then the determining equations,restriction equations and structure equations of the system are given,and conserved quantities of Lie symmetry of the system are established.Research on the lie symmetry of a singular system with nonholonomic constrains of Chetaev's type on time scales.Considering the system contains Chetaev's type nonholonomic constraints,the differential equations of motion of the system are deduced.The determining equations,restriction equations,additional restriction equations and structure equations of the system are given.The definitions of strong Lie symmetry and weak Lie symmetry are given.Then,the conserved quantities of Lie symmetry of the system are established.Research on the lie symmetry of Hamilton canonical equations in a singular system on time scales.By introducing canonical Hamilton function and generalized momentum on time scales,Considering the system contains the second kind of constraints,the regular form of motion equations of the system are derived.The determining equations,restriction equations,additional restriction equations and structure equations of the system are established.Then,the conserved quantities of Lie symmetry of the system are deduced.