The algorithms for constructing the boundaries of the stability regions of linear hamiltonian systems by using MATLAB
The article presents the main stages of the algorithm for constructing the stability regions of dynamical systems described by a linear Hamiltonian system of the form . The algorithm is based on the methods of the theory of nonlinear oscillations of stability studies of stationary solutions of linea...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | Russian |
| Published: |
The Fund for Promotion of Internet media, IT education, human development «League Internet Media»
2017-12-01
|
| Series: | Современные информационные технологии и IT-образование |
| Subjects: | |
| Online Access: | http://sitito.cs.msu.ru/index.php/SITITO/article/view/271 |
| _version_ | 1818846463309905920 |
|---|---|
| author | Marat G. Yumagulov Anna S. Belova |
| author_facet | Marat G. Yumagulov Anna S. Belova |
| author_sort | Marat G. Yumagulov |
| collection | DOAJ |
| description | The article presents the main stages of the algorithm for constructing the stability regions of dynamical systems described by a linear Hamiltonian system of the form . The algorithm is based on the methods of the theory of nonlinear oscillations of stability studies of stationary solutions of linear differential equations with periodic coefficients depending on a small parameter. The algorithm is implemented by using Matlab CAS. As an application, we have solved the problem of constructing the stability region of libration points of a flat elliptic restricted three-body problem is analyzed in detail. |
| first_indexed | 2024-12-19T05:45:57Z |
| format | Article |
| id | doaj.art-2a5e940711444a89af4390ad6cbac839 |
| institution | Directory Open Access Journal |
| issn | 2411-1473 |
| language | Russian |
| last_indexed | 2024-12-19T05:45:57Z |
| publishDate | 2017-12-01 |
| publisher | The Fund for Promotion of Internet media, IT education, human development «League Internet Media» |
| record_format | Article |
| series | Современные информационные технологии и IT-образование |
| spelling | doaj.art-2a5e940711444a89af4390ad6cbac8392022-12-21T20:33:50ZrusThe Fund for Promotion of Internet media, IT education, human development «League Internet Media»Современные информационные технологии и IT-образование2411-14732017-12-0113427027510.25559/SITITO.2017.4.525The algorithms for constructing the boundaries of the stability regions of linear hamiltonian systems by using MATLABMarat G. Yumagulov 0Anna S. Belova 1Bashkir State University, RussiaBashkir State University, RussiaThe article presents the main stages of the algorithm for constructing the stability regions of dynamical systems described by a linear Hamiltonian system of the form . The algorithm is based on the methods of the theory of nonlinear oscillations of stability studies of stationary solutions of linear differential equations with periodic coefficients depending on a small parameter. The algorithm is implemented by using Matlab CAS. As an application, we have solved the problem of constructing the stability region of libration points of a flat elliptic restricted three-body problem is analyzed in detail.http://sitito.cs.msu.ru/index.php/SITITO/article/view/271Hamiltonian systemsstabilitythe stability regionperiodic solutionsparameterthe three-body problem |
| spellingShingle | Marat G. Yumagulov Anna S. Belova The algorithms for constructing the boundaries of the stability regions of linear hamiltonian systems by using MATLAB Современные информационные технологии и IT-образование Hamiltonian systems stability the stability region periodic solutions parameter the three-body problem |
| title | The algorithms for constructing the boundaries of the stability regions of linear hamiltonian systems by using MATLAB |
| title_full | The algorithms for constructing the boundaries of the stability regions of linear hamiltonian systems by using MATLAB |
| title_fullStr | The algorithms for constructing the boundaries of the stability regions of linear hamiltonian systems by using MATLAB |
| title_full_unstemmed | The algorithms for constructing the boundaries of the stability regions of linear hamiltonian systems by using MATLAB |
| title_short | The algorithms for constructing the boundaries of the stability regions of linear hamiltonian systems by using MATLAB |
| title_sort | algorithms for constructing the boundaries of the stability regions of linear hamiltonian systems by using matlab |
| topic | Hamiltonian systems stability the stability region periodic solutions parameter the three-body problem |
| url | http://sitito.cs.msu.ru/index.php/SITITO/article/view/271 |
| work_keys_str_mv | AT maratgyumagulov thealgorithmsforconstructingtheboundariesofthestabilityregionsoflinearhamiltoniansystemsbyusingmatlab AT annasbelova thealgorithmsforconstructingtheboundariesofthestabilityregionsoflinearhamiltoniansystemsbyusingmatlab AT maratgyumagulov algorithmsforconstructingtheboundariesofthestabilityregionsoflinearhamiltoniansystemsbyusingmatlab AT annasbelova algorithmsforconstructingtheboundariesofthestabilityregionsoflinearhamiltoniansystemsbyusingmatlab |