ON THE ROLLING MOTION OF CYLINDERS IN THE SURFACE OF A FLUID

Abstract

The methods of a previous paper (ref. 1) are extended to permit the evaluation of the fluid motion when a cylinder of arbitrary symmetrical section performs simple harmonic oscillations of small amplitude about a mean position with its axis of symmetry level with the surface. Special attention is paid to the slow motions, for which a method of successive approximation is developed. Applications are made to the virtual mass in slow heaving, to the determination of the roll axis, and to motion in a sea-way. Finally, the waves generated by the forced rolling motion are studied. It is shown that their amplitude, and thus also the damping decrement, depends critically on the details of the section. A section is calculated whose rolling is undamped to the first order. Experiments are needed.