Generalized canonical transformation for second-order Birkhoffian systems on time scales  

作　　者：Y.Zhang X.H.Zhai 

机构地区：[1]college of civil engineering,suzhou university of science and technology,suzhou 215011,china [2]school of science,nanjing university of science and technology,nanjing 210094,china

出　　处：《Theoretical & Applied Mechanics Letters》2019年第6期353-357,共5页力学快报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grants 11972241 and 11572212)

摘　　要：The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems of continuous systems and discrete systems as well as other complex systems.In this paper,the theory of generalized canonical transformation for second-order Birkhoffian systems on time scales is proposed and studied,which extends the canonical transformation theory of Hamilton canonical equations.First,the condition of generalized canonical transformation for the second-order Birkhoffian system on time scales is established.Second,based on this condition,six basic forms of generalized canonical transformation for the second-order Birkhoffian system on time scales are given.Also,the relationships between new variables and old variables for each of these cases are derived.In the end,an example is given to show the application of the results.The theory of time scales, which unifies continuous and discrete analysis, provides a powerful mathematical tool for the study of complex dynamic systems. It enables us to understand more clearly the essential problems of continuous systems and discrete systems as well as other complex systems. In this paper, the theory of generalized canonical transformation for second-order Birkhoffian systems on time scales is proposed and studied, which extends the canonical transformation theory of Hamilton canonical equations. First, the condition of generalized canonical transformation for the second-order Birkhoffian system on time scales is established.Second, based on this condition, six basic forms of generalized canonical transformation for the second-order Birkhoffian system on time scales are given. Also, the relationships between new variables and old variables for each of these cases are derived. In the end, an example is given to show the application of the results.

关 键 词：BIRKHOFFIAN systems GENERALIZED CANONICAL transformation Time scales CALCULUS Generating function 

分 类 号：O41[理学—理论物理]