Canonical transformations of linear Hamiltonian systems
In this paper we consider the linear Hamiltonian systems of differential equations. We explore the normalization of a non-singular Hamiltonian matrix. We solve a system of matrix equations to find the generating function of the canonical transformation. In various cases we obtain the solution of the...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2024-01-01
|
| Series: | E3S Web of Conferences |
| Online Access: | https://www.e3s-conferences.org/articles/e3sconf/pdf/2024/122/e3sconf_emmft2024_04009.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1846161105620041728 |
|---|---|
| author | Titova Tatiana |
| author_facet | Titova Tatiana |
| author_sort | Titova Tatiana |
| collection | DOAJ |
| description | In this paper we consider the linear Hamiltonian systems of differential equations. We explore the normalization of a non-singular Hamiltonian matrix. We solve a system of matrix equations to find the generating function of the canonical transformation. In various cases we obtain the solution of the system of matrix equations. We get the solution of the algebraic matrix Riccati equation under certain conditions. Some properties of the Hamiltonian matrix have been proven. We get the normal form of a non-singular Hamiltonian matrix of order 4. We obtain the new method of normalization of the quadratic Hamiltonian. With this method we can investigate the stability of solutions of Hamiltonian systems. |
| format | Article |
| id | doaj-art-3b179b36af124623be949c90130b4d88 |
| institution | Kabale University |
| issn | 2267-1242 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | E3S Web of Conferences |
| spelling | doaj-art-3b179b36af124623be949c90130b4d882024-11-21T11:28:51ZengEDP SciencesE3S Web of Conferences2267-12422024-01-015920400910.1051/e3sconf/202459204009e3sconf_emmft2024_04009Canonical transformations of linear Hamiltonian systemsTitova Tatiana0Moscow State University of Civil EngineeringIn this paper we consider the linear Hamiltonian systems of differential equations. We explore the normalization of a non-singular Hamiltonian matrix. We solve a system of matrix equations to find the generating function of the canonical transformation. In various cases we obtain the solution of the system of matrix equations. We get the solution of the algebraic matrix Riccati equation under certain conditions. Some properties of the Hamiltonian matrix have been proven. We get the normal form of a non-singular Hamiltonian matrix of order 4. We obtain the new method of normalization of the quadratic Hamiltonian. With this method we can investigate the stability of solutions of Hamiltonian systems.https://www.e3s-conferences.org/articles/e3sconf/pdf/2024/122/e3sconf_emmft2024_04009.pdf |
| spellingShingle | Titova Tatiana Canonical transformations of linear Hamiltonian systems E3S Web of Conferences |
| title | Canonical transformations of linear Hamiltonian systems |
| title_full | Canonical transformations of linear Hamiltonian systems |
| title_fullStr | Canonical transformations of linear Hamiltonian systems |
| title_full_unstemmed | Canonical transformations of linear Hamiltonian systems |
| title_short | Canonical transformations of linear Hamiltonian systems |
| title_sort | canonical transformations of linear hamiltonian systems |
| url | https://www.e3s-conferences.org/articles/e3sconf/pdf/2024/122/e3sconf_emmft2024_04009.pdf |
| work_keys_str_mv | AT titovatatiana canonicaltransformationsoflinearhamiltoniansystems |