  We consider the problem of finding paths of shortest transit time between two
points (popularly known as Brachistochrone) for cylinders with off-centered
center of mass, rolling down without slip, subject solely to the force of
gravity. This problem is set up using principles of classical rigid body
dynamics and the desired path function is solved for numerically using the
method of discrete calculus of variations. We discover a distinct array of
brachistochrone trajectories for off-centered cylinders, demonstrate a critical
dependence of such paths on the initial location and orientation of cylinders'
centers of mass and bring new insights into the family of brachistochrone
problems and solutions.
