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Title: “SLIMPLECTIC” INTEGRATORS: VARIATIONAL INTEGRATORS FOR GENERAL NONCONSERVATIVE SYSTEMS

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.
Authors:
;  [1] ;  [2] ;  [3]
  1. Department of Physics, McGill University, Montreal, QC H3A 2T8 (Canada)
  2. Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125 (United States)
  3. Center for Radiophysics and Space Research, Cornell University, Ithaca, NY 14853 (United States)
Publication Date:
OSTI Identifier:
22518911
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal Letters; Journal Volume: 809; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ALGORITHMS; ASTROPHYSICS; GRAVITATIONAL RADIATION; HARMONIC OSCILLATORS; PLANETS; SATELLITES; VARIATIONAL METHODS