Slimplectic Integrators: Variational Integrators for General Nonconservative Systems

TL;DR

The paper introduces 'slimplectic' integrators, a novel numerical method that extends symplectic integrators to nonconservative systems, enabling accurate long-term simulations of dissipative astrophysical phenomena.

Contribution

It develops a variational integrator formalism for nonconservative systems, allowing energy and momentum tracking in systems with dissipative effects.

Findings

Successfully applied to damped harmonic oscillators

Demonstrated effectiveness with Poynting-Robertson drag

Code available for broader use

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, 2013; Galley, Tsang & Stein, 2014. 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.