Symmetries And Conserved Quantities Of Mechanical Systems For Variable Mass Holonomic Systems Of Relative Motion

Taking the whole theory of symmetries and conserved quantities of mechanical systems for variable mass holonomic systems of relative motion as the centre, the paper chiefly discusses Mei conserved quantity directly deduced from Mei symmetry, Noether conserved quantity directly deduced from Noether symmetry, and generalized Hojman conserved quantity directly deduced from Lie symmetry of Nielsen equations and Appell equations for variable mass holonomic systems of relative motion.In1935, Nielsen obtained a new type of equations for holonomic systems in his writing, which are called Nielsen equations. So far, the study of symmetries and conserved quantities for Nielsen systems has made great progress, and it has a broad developing space.In1899, a famous French mathematician Appell got an equation of motion of mechanical system different from others’ essentially, which are Appell equations. From then on, Appell equations had turned into one of the basic mechanical systems of analytical mechanics. over half a century, domestic scholars Mei Feng-Xiang,Qiao Yong-Fen, Jia Li Qun,Li Yuan-Cheng,etc have made a lot of important achievements.Moreover, scholars Mei Feng-Xiang and so on did a lot of research on variable mass systems, which improve and develop various thoeries of dynamics for variable mass holonomic systems and put forward the research on variable mass systems to a new level.The paper will continue to study the symmetries and conserved quantities of Nielsen system and Appell system and achieve important resuls.In the first chapter, first, chiefly summarize the history, the research satus and development prospect for the symmetries and conserved quantities of domenstic and foreign scholars. Second, we discuss the theoretical and practical significance of establishing the subject. At last, we simply intruduce the aim and specific content for the research of this paper.In the second chapter, we chiefly bring in the essential concept and essential theorem involving in the research content of this paper.In the third chapter, chiefly discuss the inner relation between the symmetries and conserved quantities of Nielsen equations for a variable mass holonomic system of relative motion.In the fourth chapter, chiefly discuss the inner relation between the symmetries and conserved quantities of Appell equations for a variable mass holonomic system of relative motion. In the fifth chapter, chiefly sum up the primary research work and basing on previous results, explore the potential research contents.