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: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/8070658 |
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| _version_ | 1832567175778402304 |
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| author | Xiang-Hua Zhai Yi Zhang |
| author_facet | Xiang-Hua Zhai Yi Zhang |
| author_sort | Xiang-Hua Zhai |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-73cf087d10f843089474b5a18dacae39 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-73cf087d10f843089474b5a18dacae392025-02-03T01:02:15ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/80706588070658Hamilton-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 |
| spellingShingle | Xiang-Hua Zhai Yi Zhang Hamilton-Jacobi Method for Mechanical Systems on Time Scales Complexity |
| title | 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_short | Hamilton-Jacobi Method for Mechanical Systems on Time Scales |
| title_sort | hamilton jacobi method for mechanical systems on time scales |
| url | http://dx.doi.org/10.1155/2018/8070658 |
| work_keys_str_mv | AT xianghuazhai hamiltonjacobimethodformechanicalsystemsontimescales AT yizhang hamiltonjacobimethodformechanicalsystemsontimescales |