Chapter 5: Fiber Trajectories on Shells of Revolution—An Engineering Approach

This chapter outlines a method for mathematically describing fiber trajectories on a shell of revolution. After a short outline of the basic geometry of shells of revolution, the focus shifts to fiber trajectories and their characteristic metrics, angles, and vectors. Next, the chapter focuses on the determination of various kinds of curvatures that eventually lead to the derivation of (non-) geodesic fiber trajectories according to a predetermined coefficient of friction. It concludes with the analysis of nongeodesics on conical segments, annuli, and cylinders.