The library suite JuliaStellarDynamics calculates stellar dynamics, including orbital transformations, basis expansions, finite Hilbert transforms, and linear response. The OrbitalElements.jl library transforms orbital coordinates in arbitrary central potentials and computes actions, frequencies, and resonance coordinates. AstroBasis.jl constructs and evaluates biorthogonal potential–density bases for spherical and disc systems, with support for user-defined bases. The library FiniteHilbertTransform.jl implements the finite Hilbert transform following Landau’s prescription using Legendre polynomials. Finally, LinearResponse.jl combines these tools to build response matrices and locate dynamical modes in the complex plane via Fourier-transformed basis elements, auxiliary functions, and the finite Hilbert transform. The JuliaStellarDynamics suite also offers interactive Colab notebooks that demonstrate key workflows without local installation.

EXP performs and analyzes N-body simulations using biorthogonal and orthogonal expansions. The package also supports time series analysis of expansion coefficients using multivariate Singular Spectrum Analysis (mSSA) to discover new dynamical correlations, separate signal from noise, and visualize these in two- and three-dimensional renderings. EXP's object-oriented design enforces minimal consistency while retaining flexibility.

lintsampler performs linear interpolant sampling to create a set of sample points from a density function. The code uses the evaluation of the density at the two endpoints of 1D interval, or the four corners of a 2D rectangle, or generally the 2^k vertices of a dimensional hyperbox (or a series of such hyperboxes, e.g., the cells of a k-dimensional grid) to draw random samples within the hyperbox. lintsampler works by evaluating a given PDF on the nodes of a grid (or grid-like structure, such as a tree); the number of evaluations (and memory occupancy) grows exponentially with the number of dimensions.