OrbitalElements.jl

Galactic dynamics orbits in Julia

Sample potentials

OrbitalElements ships with a handful of simple potentials and distribution functions for testing purposes. These are located in src/Potential: (1) the 3d Isochrone potential, (2) the 3d Plummer potential, (3) the 2d Mestel-Zang disc, and (4) the 2d Kuzmin-Toomre disc. Corresponding distribution functions are located in src/DistributionFunctions.

Obtaining Orbital Frequencies

The principal use for OrbitalElements is to provide descriptions of orbits. This means

1. Conversion from (semimajor axis, eccentricity) to (pericentre, apocentre) to (energy, angular momentum), to coordinates aligned with resonance vectors.
2. Additional support for actions and angles.

ComputeFrequenciesAE(ψ,dψ,d2ψ,a,e) will compute frequencies (Ω₁,Ω₂) given a potential (ψ) plus two derivatives (dψ,d2ψ), for an orbit described by semimajor axis and eccentricity.

Mapping to Resonance Space

For a given potential, one can also compute the resonance mappings, called (u,v). See src/Resonance for associated conversions. UVFromαβ(α,β,n₁,n₂,ωmin,ωmax) will compute the resonant mappings (u,v) for a given frequency pair (α,β), resonance vector (n₁,n₂), and frequency limits.

Notes

By default, OrbitalElements uses semimajor axis and eccentricity. If you want to use pericentre and apocentre, transformations are available. AEFromRpRa(rp,ra) will return semimajor axis and eccentricity from pericentre and apocentre.

OrbitalElements also uses the Henon (1971) technique to cure radial velocity divergences at peri- and apocentre.