Rotatory and Longitudinal Oscillations of Axi-Symmetric Bodies in a Viscous Fluid

The Stokes stream function is used to obtain the perturbations arising from the slow rotatory and longitudinal oscillations of axi-symmetrical bodies in an infinite mass of viscous fluid which is at rest at infinity. The bodies considered in this paper are a sphere, an infinite circular cylinder, a prolate spheroid, an oblate spheroid, and a circular disk. The case of the circular disk is deduced as a limiting case of the oblate spheroid. The paper has been divided into two parts. Part I deals with the rotatory oscillations and Part II with the longitudinal ones.