Smart: A program to automatically compute accelerations and variational equations

TL;DR

Smart is an automated tool that computes accelerations and variational equations for complex astronomical potentials written in Fortran 77, simplifying the derivation process for orbit analysis.

Contribution

The paper introduces Smart, a fully automated routine that generates Fortran 77 routines for derivatives of arbitrary potentials, including complex and time-dependent ones.

Findings

Successfully validated with diverse potential models.

Handles complex, time-dependent, and velocity-dependent potentials.

Produces ready-to-use Fortran 77 routines.

Abstract

Modern astronomical potentials modeling galaxies or stellar systems can be rather involved, and deriving their first derivatives (accelerations) and second derivatives (variational equations) in order to compute orbits and their chaoticity may be a formidable task. We present here a fully automated routine, dubbed Smart, with which the accelerations and the variational equations of an arbitrary potential that has been written in the Fortran 77 language can be computed. Almost any Fortran 77 statement is admitted in the potential, and the output are standard Fortran 77 routines ready to use. We validate our algorithm with a set of potentials including time-dependent, velocity-dependent and very complex potentials that even involve auxiliary routines. We also describe with some detail a realistic seven-component Galactic potential, MilkyWayHydra, which yields very involved derivatives, thus being a good test bed for Smart.