“SLIMPLECTIC” INTEGRATORS: VARIATIONAL INTEGRATORS FOR GENERAL NONCONSERVATIVE SYSTEMS

David Tsang, Chad R. Galley, Leo C. Stein, Alec Turner

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9 Citations (Scopus)

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.
Original languageEnglish
Article numberL9
Pages (from-to)1-6
Number of pages6
JournalAstrophysical Journal Letters
Volume809
Issue number1
Early online date6 Aug 2015
DOIs
Publication statusPublished - 10 Aug 2015

Keywords

  • celestial mechanics
  • methods: numerical
  • planets and satellites: dynamical evolution and stability

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