In this work, the dynamics of inertial (mass and moment of inertia) active Brownian particles trapped in a harmonic well is studied. This scenario has seen success when characterizing soft passive and active overdamped matter. Motivated by the variety of applications of this system, we analytically find the effect of translational and rotational inertia on the mean-square displacement (MSD), mean-square speed (MSS), swim, Reynolds, and total pressures of a system of inertial active Brownian particles subject to a weak and a strong harmonic trap. Following a Langevin formalism, we explicitly find that as inertia grows, the systems' MSD and total pressure are enhanced, but its MSS and swim pressure decrease. The use of Langevin dynamics simulations enables us to observe that as inertia grows, inertial active matter under a strong trap no longer "condensates" at the "border" of the trap, but it rather tends to uniformly spread in space. Our analytical results are also numerically validated.
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