LINEAR AND NONLINEAR DYNAMICS OF CANTILEVERED CYLINDERS IN AXIAL FLOW. PART 2: THE EQUATIONS OF MOTION

In this paper a nonlinear equation of motion is derived for the dynamics of a slender cantilevered cylinder in axial flow, generally terminated by an ogival free end. Inviscid forces are modelled by an extension of Lighthill's slender-body work to third-order accuracy. The viscous, hydrostatic and gravity-related terms are derived separately, to the same accuracy. The equation of motion is obtained via Hamilton's principle. The boundary conditions related to the ogival free end are also derived separately. The paper is concluded by a discussion of the methods used to obtain the solutions presented in Part 3 of this study.