Study On NLM Symmetries And Conserved Quantities For Discrete Mechanical Systems In Event Space

The theory of symmetries and conserved quantities is very important to understand the physical state and the properties of the system.The researches on the theory of symmetries and conserved quantities of discrete mechanical system have important theoretical value and practical significance.In this paper,we study the symmetries and their resulting conserved quantities of discrete mechanical system in event space with the difference discrete variational approach of variable time step,based on the theory of symmetries and conserved quantities of continuous mechanical system.Firstly,the theories of Noether symmrtries,Lie symmrtries and and Mei symmrtries for discrete holonomic conservative systems and non-conservative systems in event space are established.The conditions and the formulations of conserved quantities are obtained directly from Noether symmrtries,Lie symmrtries and and Mei symmrtries.The conditions and the formulations of conserved quantities are obtained indirectly from the three kinds of symmrtries mentioned above,based on the relationship between Noether symmrtries,Lie symmrtries and and Mei symmrtries.Secondly,the theories of Noether symmrtries,Lie symmrtries and and Mei symmrtries for discrete Chetaev nonholonomic systems in event space are established.The conditions and the formulations of conserved quantities are obtained directly from Noether symmrtries,Lie symmrtries and and Mei symmrtries.The conditions and the formulations of conserved quantities are obtained indirectly from the three kinds of symmrtries mentioned above,based on the relationship between Noether symmrtries,Lie symmrtries and and Mei symmrtries.Finally,the theories of Noether symmrtries,Lie symmrtries and and Mei symmrtries for discrete nonholonomic systems of variable mass in event space are established.The conditions and the formulations of conserved quantities are obtained directly from Noether symmrtries,Lie symmrtries and and Mei symmrtries.The conditions and the formulations of conserved quantities are obtained indirectly from the three kinds of symmrtries mentioned above,based on the relationship between Noether symmrtries,Lie symmrtries and and Mei symmrtries.