Symplectic integration for the collisional gravitational
We present a new symplectic integrator designed for collisional gravitational N-body problems which makes use of Kepler solvers. The integrator is also reversible and conserves nine integrals of motion of the N-body problem to machine precision. The integrator is second order, but the order can easi...
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| Format: | Article |
| Language: | en_US |
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Oxford University Press
2017
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| Online Access: | http://hdl.handle.net/1721.1/108694 https://orcid.org/0000-0001-7648-0926 https://orcid.org/0000-0003-2480-5973 |
| _version_ | 1826198147319201792 |
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| author | Hernandez, David Michael Bertschinger, Edmund |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Hernandez, David Michael Bertschinger, Edmund |
| author_sort | Hernandez, David Michael |
| collection | MIT |
| description | We present a new symplectic integrator designed for collisional gravitational N-body problems which makes use of Kepler solvers. The integrator is also reversible and conserves nine integrals of motion of the N-body problem to machine precision. The integrator is second order, but the order can easily be increased by the method of Yoshida. We use fixed time step in all tests studied in this paper to ensure preservation of symplecticity. We study small N collisional problems and perform comparisons with typically used integrators. In particular, we find comparable or better performance when compared to the fourth-order Hermite method and much better performance than adaptive time step symplectic integrators introduced previously. We find better performance compared to SAKURA, a non-symplectic, non-time-reversible integrator based on a different two-body decomposition of the N-body problem. The integrator is a promising tool in collisional gravitational dynamics. |
| first_indexed | 2024-09-23T10:59:45Z |
| format | Article |
| id | mit-1721.1/108694 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:59:45Z |
| publishDate | 2017 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | mit-1721.1/1086942022-09-27T16:25:00Z Symplectic integration for the collisional gravitational Hernandez, David Michael Bertschinger, Edmund Massachusetts Institute of Technology. Department of Physics MIT Kavli Institute for Astrophysics and Space Research Hernandez, David Michael Bertschinger, Edmund W We present a new symplectic integrator designed for collisional gravitational N-body problems which makes use of Kepler solvers. The integrator is also reversible and conserves nine integrals of motion of the N-body problem to machine precision. The integrator is second order, but the order can easily be increased by the method of Yoshida. We use fixed time step in all tests studied in this paper to ensure preservation of symplecticity. We study small N collisional problems and perform comparisons with typically used integrators. In particular, we find comparable or better performance when compared to the fourth-order Hermite method and much better performance than adaptive time step symplectic integrators introduced previously. We find better performance compared to SAKURA, a non-symplectic, non-time-reversible integrator based on a different two-body decomposition of the N-body problem. The integrator is a promising tool in collisional gravitational dynamics. National Science Foundation (U.S.). Graduate Research Fellowship Program (Grant 1122374) 2017-05-05T14:40:31Z 2017-05-05T14:40:31Z 2015-07 2015-06 Article http://purl.org/eprint/type/JournalArticle 0035-8711 1365-2966 http://hdl.handle.net/1721.1/108694 Hernandez, David M., and Edmund Bertschinger. “Symplectic Integration for the Collisional Gravitational N -Body Problem.” Monthly Notices of the Royal Astronomical Society 452.2 (2015): 1934–1944. https://orcid.org/0000-0001-7648-0926 https://orcid.org/0000-0003-2480-5973 en_US http://dx.doi.org/10.1093/mnras/stv1439 Monthly Notices of the Royal Astronomical Society Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Oxford University Press arXiv |
| spellingShingle | Hernandez, David Michael Bertschinger, Edmund Symplectic integration for the collisional gravitational |
| title | Symplectic integration for the collisional gravitational |
| title_full | Symplectic integration for the collisional gravitational |
| title_fullStr | Symplectic integration for the collisional gravitational |
| title_full_unstemmed | Symplectic integration for the collisional gravitational |
| title_short | Symplectic integration for the collisional gravitational |
| title_sort | symplectic integration for the collisional gravitational |
| url | http://hdl.handle.net/1721.1/108694 https://orcid.org/0000-0001-7648-0926 https://orcid.org/0000-0003-2480-5973 |
| work_keys_str_mv | AT hernandezdavidmichael symplecticintegrationforthecollisionalgravitational AT bertschingeredmund symplecticintegrationforthecollisionalgravitational |