Symmetries And Conserved Quantities For Constrained Mechanical Systems In Event Space

This dissertation is devoted to the problems of symmetries and conserved quantities for nonholonomic systems, nonholonomic systems of variable mass and nonholonomic systems of relative motion in event space, including Noether symmetries, Lie symmetries, form invariances, unified symmetries and united symmetries. First, the theories of Noether symmetries, Lie symmetries and form invariances for nonholonomic systems in event space are established. Then, the relationship between Lie symmetry and Noether symmetry as well as Lie symmetry and form invariance is studied. The conditions and the formulations of conserved quantities are obtained directly or indirectly from the three kinds of symmetries mentioned above. Then, the definitions of unified symmetries for nonholonomic system in event space are presented, and the conditions and the formulations of conserved quantities are obtained directly from unified symmetries. Second, the theories of Noether symmetries, Lie symmetries, form invariances and unified symmetries for nonholonomic systems of variable mass in event space are investigated. Then, the conditions and the formulations of conserved quantities are obtained directly from the four kinds of symmetries mentioned above. Finally, the theories of Noether symmetries, Lie symmetries and form invariances for nonholonomic systems of relative motion in event space are discussed. The conditions and the formulations of conserved quantities are obtained directly from the three kinds of symmetries mentioned above. Then, the definitions of united symmetries for nonholonomic system of relative motion in event space are given, including Noether-Lie symmetries, Noether- form invariances and Lie-form invariances, and the conditions and the formulations of conserved quantities are obtained directly from united symmetries.