  Asymmetrically charged, nonspherical colloidal particles in general perform
complex rotations and oblique motions under an electric field. The interplay of
electrostatic and hydrodynamic forces complicate the prediction of these
motions. We demonstrate a method of calculating the body tensors that dictate
translational and rotational velocity vectors arising from an external electric
field. We treat insulating, rigid bodies in the linear-response regime, with
indefinitely small electrostatic screening length. The method represents the
body as an assembly of point sources of both hydrodynamic drag and surface
electric field. We demonstrate agreement with predicted electrophoretic
mobility to within a few percent for several shapes with uniform and nonuniform
charge. We demonstrate strong chiral twisting motions for colloidal bodies of
symmetrical realistic shapes. The method applies more generally to active
colloidal swimmers.
