Hamilton-Jacobi Method for Mechanical Systems on Time Scales

Hamilton-Jacobi Method for Mechanical Systems on Time Scales

This paper presents the Hamilton-Jacobi method for integrating the equations of motion of mechanical systems on time scales. We give the criterion and four basic forms of canonical transformation on time scales. Also, various examples are given to illustrate the role played by a generating function...

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Main Authors: Xiang-Hua Zhai, Yi Zhang
Format: Article
Language:English
Published: Hindawi-Wiley 2018-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2018/8070658
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spelling doaj-73cf087d10f843089474b5a18dacae392020-11-25T00:58:58ZengHindawi-WileyComplexity1076-27871099-05262018-01-01201810.1155/2018/80706588070658Hamilton-Jacobi Method for Mechanical Systems on Time ScalesXiang-Hua Zhai0Yi Zhang1School of Science, Nanjing University of Science and Technology, Nanjing 210094, ChinaCollege of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, ChinaThis paper presents the Hamilton-Jacobi method for integrating the equations of motion of mechanical systems on time scales. We give the criterion and four basic forms of canonical transformation on time scales. Also, various examples are given to illustrate the role played by a generating function in the canonical transformation. By choosing an appropriate generating function, we construct the Hamilton-Jacobi equation on time scales and prove the Jacobi theorem on time scales. An example for an Emden-Fowler type equation is discussed to show the application of the method.http://dx.doi.org/10.1155/2018/8070658
collection DOAJ
language English
format Article
sources DOAJ
author Xiang-Hua Zhai
Yi Zhang
spellingShingle Xiang-Hua Zhai
Yi Zhang
Hamilton-Jacobi Method for Mechanical Systems on Time Scales
Complexity
author_facet Xiang-Hua Zhai
Yi Zhang
author_sort Xiang-Hua Zhai
title Hamilton-Jacobi Method for Mechanical Systems on Time Scales
title_short Hamilton-Jacobi Method for Mechanical Systems on Time Scales
title_full Hamilton-Jacobi Method for Mechanical Systems on Time Scales
title_fullStr Hamilton-Jacobi Method for Mechanical Systems on Time Scales
title_full_unstemmed Hamilton-Jacobi Method for Mechanical Systems on Time Scales
title_sort hamilton-jacobi method for mechanical systems on time scales
publisher Hindawi-Wiley
series Complexity
issn 1076-2787
1099-0526
publishDate 2018-01-01
description This paper presents the Hamilton-Jacobi method for integrating the equations of motion of mechanical systems on time scales. We give the criterion and four basic forms of canonical transformation on time scales. Also, various examples are given to illustrate the role played by a generating function in the canonical transformation. By choosing an appropriate generating function, we construct the Hamilton-Jacobi equation on time scales and prove the Jacobi theorem on time scales. An example for an Emden-Fowler type equation is discussed to show the application of the method.
url http://dx.doi.org/10.1155/2018/8070658
work_keys_str_mv AT xianghuazhai hamiltonjacobimethodformechanicalsystemsontimescales
AT yizhang hamiltonjacobimethodformechanicalsystemsontimescales
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