A note on the S-transform and slender body theory in Stokes flow

The slender body transform, known in abbreviated form as the S-transform, arises naturally from the asymptotic analysis of very viscous flow around slender bodies. This paper considers some of the properties of the S-transform as well as exploiting the special properties associated with Legendre polynomials to generate a range of slender body shapes with fixed drag. The viable parameter space for these examples is also presented.