Mei Symmetry And Mei Conserved Quantity For Constrained Mechanical Systems

Focusing on the integral theory of Mei symmetry for constraint dynamical systems, mainly study the Mei symmetry and the Mei conserved quantity in Appell systems and Nielsen systems.In resent years, most of the researches about symmetries and conserved quantities are mainly limited to the situation about the bilateral constraints[and a very little work has been done to the situation about the unilateral constraints.Besides, the study on both symmetry and conserved quantity in Appell style is very slow. In 2008, Jia extended the new expression of the total derivative of function with respective to t along the curve of motion of the system and first solved the problem how to look for the structure equation and the expression of Mei conserved quantity which can be denoted as Appell function. But up to now the new method haven't got effective extended. Therefore, the problem of Mei symmetry of Appell equantions still need to be further improved.The study of this paper improved the problem of the Mei symmetry and Mei conserved quantity in Nielsen systems and made up shortages in Appell function. We got the important achievements that the predecessors have not yet received.The chapters are arranged as following:In chapter 1, a general discussion of the historical development, as well as the current research of the symmetries and conserved quantities at home and abroad. The significance, purpose and content of the research of this paper.In chapter 2, the author introduces the basic concept and basic theory of the research in this article.In chapter 3, mainly study the Mei symmetry and Mei conserved quantity in Nielsen systems. First, the differential equations of motion in Nielsen systems are established. Second, the definitions and the criterion equations are given. Finally, the structure equation of Mei symmetry and the expression of Mei conserved quantity are achieved.In chapter 4, mainly study the Mei symmetry and Mei conserved quantity in Appell systems. First, Appell equations and the differential equations of motion are established. Second, a new expression of the total derivative of function with respective to t along the curve of motion of the systems is given, and the definitions of Mei symmetry of Appell equations under the infinitesimal transformations of groups are obtained, and the criterion equations corresponding to the systems are also gained. Finally, the structure equation of Mei symmetry and the expression of Mei conserved quantity in Appell function are extended.In chapter 5, we summarize the main results of our research and envision the future research directions.