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

作     者：Y.Zhang X.H.Zhai 

作者机构：college of civil engineeringsuzhou university of science and technologysuzhou 215011china school of sciencenanjing university of science and technologynanjing 210094china 

出 版 物：《Theoretical & Applied Mechanics Letters》 (力学快报（英文版）)

年 卷 期：2019年第9卷第6期

页      面：353-357页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 0801[工学-力学（可授工学、理学学位）] 

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

主　　题：Birkhoffian systems Generalized canonical transformation Time scales calculus Generating function 

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.