Force-dependence of the rigid-body motion for an arbitrarily shaped particle in a forced, incompressible Stokes flow

A rigid body immersed in a fluid will generically move when the latter experiences a local force field. In the creeping flow regime, the body velocities (translational and angular) will be linear functionals of this field (``force representation''). Due to the incompressibility constraint, however, it should be possible to express them equivalently as linear functionals of the curl of the force (``curl representation''). Explicit expressions for this alternative formulation are derived, and illustrated with the example of self-chemophoresis.