Schematic flowchart of the OTIS library. The code workflow starts with the initialisation of the DM halo parameters, including the concentration parameter and virial quantities, eventually followed by the initialisation of the stellar Hernquist bulge. The density, mass, and velocity dispersion profiles of both the halo and the bulge can be hence retrieved. The BH can then be initialised with its mass and phase-space coordinates. The integral of the velocity distribution function is pre-computed on a phase-space grid, enabling fast interpolation during the numerical integration of the equations of motion. User-configurable options enable the customisation of the interpolation technique, integration method, time steps, and impact parameters.