Symmetries And Conserved Quantities Of The Singular Systems

This dissertation is devoted to the study of symmetries and conserved quantities for singular nonholonomic systems, including Noether symmetries, Lie symmetries, Mei symmetries, united symmetries and unified symmetries.Under the infinitesimal transformation of groups, the theory of Noether symmetries, Lie symmetries and Mei symmetries for the systems which are singular nonholonomic systems, singular nonholonomic systems of variable mass systems, singular noholonomic system with unilateral constraints, Nielsen Equations for singular noholonomic system and singular noholonomic mechanico-electrical system are established. The conditions and the formulations of conserved quantities are obtained from the three kinds of symmetries mentioned above. Second, the theory of united symmetries for the systems which are singular nonholonomic systems, singular nonholonomic systems of variable mass systems, singular noholonomic system with unilateral constraints, Nielsen Equations for singular noholonomic system and singular noholonomic mechanico-electrical system are established, including Noether-Lie symmetries, Noether-Mei symmetries and Lie-Mei symmetries. The definitions and the criterions of united symmetries are given. The conditions and the formulations of conserved quantities are obtained from the united symmetries mentioned above. Finally, the theory of unified symmetries for the systems mentioned above is studied. Then, the definitions and the criterions of united symmetries are given. The conditions and the formulations of conserved quantities are obtained.