Analytical Solution to Normal Forms of Hamiltonian Systems
The idea of the normalisation of the Hamiltonian system is to simplify the system by transforming Hamiltonian canonically to an easy system. It is under symplectic conditions that the Hamiltonian is preserved under a specific transformation—the so-called Lie transformation. In this review, we will s...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2017-07-01
|
| Series: | Mathematical and Computational Applications |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2297-8747/22/3/37 |
| _version_ | 1828380322376450048 |
|---|---|
| author | Ali Allahem |
| author_facet | Ali Allahem |
| author_sort | Ali Allahem |
| collection | DOAJ |
| description | The idea of the normalisation of the Hamiltonian system is to simplify the system by transforming Hamiltonian canonically to an easy system. It is under symplectic conditions that the Hamiltonian is preserved under a specific transformation—the so-called Lie transformation. In this review, we will show how to compute the normal form for the Hamiltonian, including computing the general function analytically. A clear example has been studied to illustrate the normal form theory, which can be used as a guide for arbitrary problems. |
| first_indexed | 2024-12-10T03:54:53Z |
| format | Article |
| id | doaj.art-bcffd70c9bcc40339901184145e02432 |
| institution | Directory Open Access Journal |
| issn | 2297-8747 |
| language | English |
| last_indexed | 2024-12-10T03:54:53Z |
| publishDate | 2017-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-bcffd70c9bcc40339901184145e024322022-12-22T02:03:09ZengMDPI AGMathematical and Computational Applications2297-87472017-07-012233710.3390/mca22030037mca22030037Analytical Solution to Normal Forms of Hamiltonian SystemsAli Allahem0Department of Mathematics, College of Sciences, Qassim University, P.O. Box 6666, Buraydah 51452, Saudi ArabiaThe idea of the normalisation of the Hamiltonian system is to simplify the system by transforming Hamiltonian canonically to an easy system. It is under symplectic conditions that the Hamiltonian is preserved under a specific transformation—the so-called Lie transformation. In this review, we will show how to compute the normal form for the Hamiltonian, including computing the general function analytically. A clear example has been studied to illustrate the normal form theory, which can be used as a guide for arbitrary problems.https://www.mdpi.com/2297-8747/22/3/37Hamiltoniannormal formsgenerating functionLie transformationcanonical transformation |
| spellingShingle | Ali Allahem Analytical Solution to Normal Forms of Hamiltonian Systems Mathematical and Computational Applications Hamiltonian normal forms generating function Lie transformation canonical transformation |
| title | Analytical Solution to Normal Forms of Hamiltonian Systems |
| title_full | Analytical Solution to Normal Forms of Hamiltonian Systems |
| title_fullStr | Analytical Solution to Normal Forms of Hamiltonian Systems |
| title_full_unstemmed | Analytical Solution to Normal Forms of Hamiltonian Systems |
| title_short | Analytical Solution to Normal Forms of Hamiltonian Systems |
| title_sort | analytical solution to normal forms of hamiltonian systems |
| topic | Hamiltonian normal forms generating function Lie transformation canonical transformation |
| url | https://www.mdpi.com/2297-8747/22/3/37 |
| work_keys_str_mv | AT aliallahem analyticalsolutiontonormalformsofhamiltoniansystems |