Fokker-Planck description of an active Brownian particle with rotational inertia

We develop a perturbative framework to calculate the mean-squared displacement (MSD) of active Brownian particles (ABPs) with a finite moment of inertia. Starting from the corresponding Fokker-Planck equation, we employ a Fourier transform for the spatial coordinates and Hermite polynomials as eigenfunctions for the angular velocity, which enables a systematic perturbative expansion of the MSD order by order. By resumming the resulting series in Laplace space and performing the inverse transform, we obtain an explicit expression for the MSD as a function of the moment of inertia. The analytical results are further validated by comparison with numerical simulations.