Slow motion of a Cassinian cylinder in a viscous fluid

The Stokes problem of the motion of a cylinder in a viscous, incompressible fluid has been formulated in this paper in the form of an integral equation for the velocity and pressure fields involving a distribution of Stokeslets on the boundary curve in the xy-plane of the cylinder. It is found that for a cylinder whose boundary curve is a member of the family of equipotential curves, this distribution is related to the linear mass density of the Newtonian potential theory and knowledge of one leads to the determination of the other.