  The motion of charged particles can be interfaced with electric circuitry via
the current induced in nearby pick-up electrodes. Here we show how the
rotational and translational dynamics of levitated objects with arbitrary
charge distributions can be coupled to a circuit and how the latter acts back
on the particle motion. The ensuing cooling rates in series and parallel RLC
circuits are determined, demonstrating that quadrupole ion traps are well
suited for implementing all-electric cooling. We derive the effective
macromotion potential for general trap geometries and demonstrate numerically
how consecutive rotational and translational resistive cooling of a microscale
particle can be achieved in linear Paul traps.
