  Mobile microscopic bodies, such as motile cells, can be modelled
phenomenologically as ``active particles'' which can move against external
forces by depleting an internal energy depot. The microscopic mechanisms
underlying such ``active'' behavior must ultimately obey fundamental physics:
energy depots must actually consist of dynamical degrees of freedom, such as
chemical reaction coordinates, which in some way couple to the particle's
motional degrees of freedom. As a step towards connecting phenomenological
models with microscopic dynamical mechanisms, recent papers have studied the
minimalistic dynamical mechanism of a ``dynamical active particle'', and shown
how nonlinear couplings can allow steady energy transfer from depot to motion,
even in the presence of weak dissipation. Most real active particles move
through viscous environments, however, and are strongly damped. Here we
therefore generalize the dynamical active particle into the overdamped regime.
We find that its mechanism still operates, and in particular allows the
overdamped active particle to travel just as far against friction as the
undamped model, by moving at a slower average speed. Our results suggest that
active particle phenomenology can indeed be consistent with comprehensible
dynamical mechanisms, even in strongly dissipative environments.
