Variable Timestep Integrators for Long-Term Orbital Integrations

TL;DR

This paper introduces a novel symplectic integrator for long-term orbital simulations that effectively handles variable timesteps by decomposing forces, maintaining conservation properties crucial for Hamiltonian systems.

Contribution

It presents a new multiple timescale symplectic integrator that preserves key properties of constant timestep methods while allowing variable timesteps for improved long-term orbital integration.

Findings

The integrator maintains symplectic properties with variable timesteps.

It improves long-term accuracy in orbital simulations.

The method decomposes forces to handle different timescales effectively.

Abstract

Symplectic integration algorithms have become popular in recent years in long-term orbital integrations because these algorithms enforce certain conservation laws that are intrinsic to Hamiltonian systems. For problems with large variations in timescale, it is desirable to use a variable timestep. However, naively varying the timestep destroys the desirable properties of symplectic integrators. We discuss briefly the idea that choosing the timestep in a time symmetric manner can improve the performance of variable timestep integrators. Then we present a symplectic integrator which is based on decomposing the force into components and applying the component forces with different timesteps. This multiple timescale symplectic integrator has all the desirable properties of the constant timestep symplectic integrators.