Study of Chaos in Rotating Galaxies Using Extended Force-Gradient Symplectic Methods
We take into account the dynamics of three types of models of rotating galaxies in polar coordinates in a rotating frame. Due to non-axisymmetric potential perturbations, the angular momentum varies with time, and the kinetic energy depends on the momenta and spatial coordinate. The existing explici...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/1/63 |
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| author | Lina Zhang Wenfang Liu Xin Wu |
| author_facet | Lina Zhang Wenfang Liu Xin Wu |
| author_sort | Lina Zhang |
| collection | DOAJ |
| description | We take into account the dynamics of three types of models of rotating galaxies in polar coordinates in a rotating frame. Due to non-axisymmetric potential perturbations, the angular momentum varies with time, and the kinetic energy depends on the momenta and spatial coordinate. The existing explicit force-gradient symplectic integrators are not applicable to such Hamiltonian problems, but the recently extended force-gradient symplectic methods proposed in previous work are. Numerical comparisons show that the extended force-gradient fourth-order symplectic method with symmetry is superior to the standard fourth-order symplectic method but inferior to the optimized extended force-gradient fourth-order symplectic method in accuracy. The optimized extended algorithm with symmetry is used to explore the dynamical features of regular and chaotic orbits in these rotating galaxy models. The gravity effects and the degree of chaos increase with an increase in the number of radial terms in the series expansions of the potential. There are similar dynamical structures of regular and chaotical orbits in the three types of models for the same number of radial terms in the series expansions, energy and initial conditions. |
| first_indexed | 2024-03-09T11:08:28Z |
| format | Article |
| id | doaj.art-c632408e4acb497a9b30e91e34b270a5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T11:08:28Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-c632408e4acb497a9b30e91e34b270a52023-12-01T00:51:14ZengMDPI AGSymmetry2073-89942022-12-011516310.3390/sym15010063Study of Chaos in Rotating Galaxies Using Extended Force-Gradient Symplectic MethodsLina Zhang0Wenfang Liu1Xin Wu2Center of Application and Research of Computational Physics, School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, ChinaCenter of Application and Research of Computational Physics, School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, ChinaCenter of Application and Research of Computational Physics, School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, ChinaWe take into account the dynamics of three types of models of rotating galaxies in polar coordinates in a rotating frame. Due to non-axisymmetric potential perturbations, the angular momentum varies with time, and the kinetic energy depends on the momenta and spatial coordinate. The existing explicit force-gradient symplectic integrators are not applicable to such Hamiltonian problems, but the recently extended force-gradient symplectic methods proposed in previous work are. Numerical comparisons show that the extended force-gradient fourth-order symplectic method with symmetry is superior to the standard fourth-order symplectic method but inferior to the optimized extended force-gradient fourth-order symplectic method in accuracy. The optimized extended algorithm with symmetry is used to explore the dynamical features of regular and chaotic orbits in these rotating galaxy models. The gravity effects and the degree of chaos increase with an increase in the number of radial terms in the series expansions of the potential. There are similar dynamical structures of regular and chaotical orbits in the three types of models for the same number of radial terms in the series expansions, energy and initial conditions.https://www.mdpi.com/2073-8994/15/1/63symplectic integratorschaosgalaxiesgravity |
| spellingShingle | Lina Zhang Wenfang Liu Xin Wu Study of Chaos in Rotating Galaxies Using Extended Force-Gradient Symplectic Methods Symmetry symplectic integrators chaos galaxies gravity |
| title | Study of Chaos in Rotating Galaxies Using Extended Force-Gradient Symplectic Methods |
| title_full | Study of Chaos in Rotating Galaxies Using Extended Force-Gradient Symplectic Methods |
| title_fullStr | Study of Chaos in Rotating Galaxies Using Extended Force-Gradient Symplectic Methods |
| title_full_unstemmed | Study of Chaos in Rotating Galaxies Using Extended Force-Gradient Symplectic Methods |
| title_short | Study of Chaos in Rotating Galaxies Using Extended Force-Gradient Symplectic Methods |
| title_sort | study of chaos in rotating galaxies using extended force gradient symplectic methods |
| topic | symplectic integrators chaos galaxies gravity |
| url | https://www.mdpi.com/2073-8994/15/1/63 |
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