Mei Conserved Quantity Deduced From Mei Symmetry Of Three Important Mechanical Systems

Focusing on the integral theory of Mei symmetry, mainly study Mei symmetry and Mei conserved quantity of a Nielsen equationfor a holonomic system in terms of quasi-coordinates, Mei symmetry and Mei conserved quantity of nonholonomic systems with Chetaev type in Nielsen style, and Structural equation and Mei conserved quantity for Mei symmetry of nonholonomic systems with Chetaev type in Appell style with variable massLagrangian system, Nielsen style and Appell style are the three important mechanical systems and occupie important position in the analytical mechanics.At present, the studies about symmetrys and conserved quantity of Nielsen equations have also made some progressBesides, 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 typeâ…¢structural equation and Mei conserved quantity of Mei symmetry for a Lagrangian system are studied. Under the infinitesimal transformation of groups, typeâ…¢structural equation and Mei conserved quantity of Mei symmetry for a Lagrangian system are obtained from the definition and the criterion of Mei symmetry for a Lagrangian system.In chapter 4, mainly study Mei conserved quantity constructed from Mei symmetry of a Nielsen equation for a holonomic system in terms of quasi-coordinates. The definition and the criterion of Mei symmetry of a Nielsen equation for a holonomic mechanical system in terms of quasi-coordinates are given, and the condition and the form of the Mei conserved quantity deduced directly from the Mei symmetry of the Nielsen equation for a holonomic mechanical system are discussed. mainly study Mei symmetry and Mei conserved quantity of Nielsen equation for a nonholonomic, non-conservative system of Chetaev's type with variable mass are studied. The differential equations of motion of Nielsen equation for the system the definition and criterion of Mei symmetry, and the condition and the form of Mei conserved quantity deduced directly by Mei symmetry for the system are obtained. In chapter 5, mainly study Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems are investigated. Appell equations and differential equations of motion for holonomic mechanic systems are established. The definition and the criterion of Mei symmetry for Appell equations under the infinitesimal transformations of groups are also given. The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems expressed by Appell functions are obtained, and structural equation and Mei conserved quantity for Mei symmetry of nonholonomic systems with Chetaev type in Appell style are studied. The differential equations of motion of Appell equation for the system, the definition and criterion of Mei symmetry, and the condition and the form of Mei conserved quantity deduced directly by Mei symmetry for the system are obtained.In chapter 6, we summarize the main results of our research and envision the future research directions.