Free Body Dynamics of a Spinning Cylinder With Planar Restraint (a.k.a. Barrel of Fun)

The dynamic motion of a cylinder on a floor or hard surface is both entertaining and instructive. With maintenance torques, motion can be sustained and controlled as illustrated in a video clip that can be viewed in the PDF file of this document. The analysis of such a cylinder with and without end caps is burned on rotation about its center of mass and restrained by a plane normal to the axis passing through its center of mass at an angle alpha. For small values of alpha, the governing equations are simplified, and for symmetric bodies, stability requires rotation greater than [2 square root of(JWL*)]/J(sub X), where J is the transverse mass moment of inertia, W is the weight of the cylinder, L* is the cylinder length from the base to the center of mass, and JX is the mass moment of inertia about the longitudinal axis OX of the barrel. Comparisons to data are made and some applications are discussed.