The Research Of NM Symmetry And Conserved Quantity For Discrete Systems In Configuration Space

The symmetry principle is the higher level rules in physics,symmetry analysis as a research method,widely used in mathematics,physics and other disciplines,it has important theoretical value and practical significance.With the development of the symmetries and conserved quantities in continuous mechanical systems,the research on symmetries and conserved quantities in discrete systems has become one of the important research directions in analytical mechanics,and shows its unique advantages in practical applications.In this paper,on the basis of the study of the symmetries and conserved quantities in continuous systems,we use the difference discrete variational approach to study the NM symmetry(Noether symmetry,Mei symmetry)and conserved quantity for discrete systems in configuration space.Firstly,using the discrete Hamilton principle and the difference discrete variational method,the continuous system are discretized and the discrete motion equations for the discrete holonomic mechanical systems,discrete nonholonomic mechanical systems and discrete variable mass system are obtained.And the discrete motion equations retain the original structure of continuous equations.Secondly,the Noether symmetry,the Mei symmetry and the conserved quantities for discrete holonomic system,discrete nonholonomic mechanical systems in configuration space are studied.The definitions and criterion equations of Noether symmetry and Mei symmetry for these two discrete systems are given.The form of the discrete Noether conserved quantity and the condition under which the Noether conserved quantity can be induced by the Noether symmetry are generated.The forms and the conditions of the discrete Mei conserved quantity,the new conserved quantity and the Noether conserved quantity deduced from Mei symmetry are obtained.Then the Noether symmetry,the Mei symmetry and the conserved quantities for discrete variable mass system in configuration space are studied.The definitions and criterion equations of Noether symmetry and Mei symmetry for the discrete system are given.The forms of the discrete Noether conserved quantity?Mei conserved quantity and the new conserved quantity are generated.And the conditions under which these three conserved quantities can be induced by the Noether symmetry and Mei symmetry are obtained.Finally,the research results of this paper are summarized and the researches on symmetry and conserved quantities for discrete systems are prospected.