"Slimplectic" integrators: variational integrators for general nonconservative systems
Abstract
Symplectic integrators are widely used for long-term integration of conservative astrophysical problems due to their ability to preserve the constants of motion; however, they cannot in general be applied in the presence of nonconservative interactions. In this Letter, we develop the "slimplectic" integrator, a new type of numerical integrator that shares many of the benefits of traditional symplectic integrators yet is applicable to general nonconservative systems. We utilize a fixed-time-step variational integrator formalism applied to the principle of stationary nonconservative action developed in Galley et al. As a result, the generalized momenta and energy (Noether current) evolutions are well-tracked. We discuss several example systems, including damped harmonic oscillators, Poynting–Robertson drag, and gravitational radiation reaction, by utilizing our new publicly available code to demonstrate the slimplectic integrator algorithm. Slimplectic integrators are well-suited for integrations of systems where nonconservative effects play an important role in the long-term dynamical evolution. As such they are particularly appropriate for cosmological or celestial N-body dynamics problems where nonconservative interactions, e.g., gas interactions or dissipative tides, can play an important role.
Additional Information
© 2015. The American Astronomical Society. We thank A. Cumming, A. Archibald, D. Tamayo, D. P. Hamilton, M. C. Miller, and the referee, W. Farr, for useful discussion. D.T. was supported by the Lorne Trottier Chair in Astrophysics and Cosmology and CRAQ. C.R.G. was supported in part by NSF grants CAREER PHY-0956189 and PHY-1404569 at Caltech. L.C.S. was supported by NASA through Einstein Postdoctoral Fellowship Award number PF2-130101.Attached Files
Published - Tsang_2015_ApJL_809_L9.pdf
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Additional details
- Eprint ID
- 120634
- Resolver ID
- CaltechAUTHORS:20230330-310853000.1
- Lorne Trottier Chair in Astrophysics and Cosmology
- Centre for Research in Astrophysics of Québec (CRAQ)
- PHY-0956189
- NSF
- PHY-1404569
- NSF
- PF2-130101
- NASA Eistein Fellowship
- Created
-
2023-03-31Created from EPrint's datestamp field
- Updated
-
2023-03-31Created from EPrint's last_modified field
- Caltech groups
- TAPIR, Walter Burke Institute for Theoretical Physics