Active Brownian motion with inertia: The role of dimensionality

The joint influence of rotational inertia and dimensionality on the translational motion of a free self-propelled (active) Brownian particle is studied. When the reduced moment of inertia is not large, the three-dimensional particle dynamics is statistically described by the equations for the two-dimensional case only with the doubled rotational diffusion coefficient. However, for large reduced moment of inertia, the three- and two-dimensional dynamics of the particle differ dramatically. It is shown that the time-dependent mean square particle displacement can be described by the active Ornstein–Uhlenbeck particle model, where the orientational persistence and momentum relaxation times are effectively corrected by the particle rotational inertia.