  A 3-parameter family of helical tubular surfaces obtained by screw revolving
a circle provides a useful pedagogical example of how to study geodesics on a
surface that admits a 1-parameter symmetry group, but is not as simple as a
surface of revolution like the torus which it contains as a special case. It
serves as a simple example of helically symmetric surfaces which are the
generalizations of surfaces of revolution in which an initial plane curve is
screw-revolved around an axis in its plane. The physics description of geodesic
motion on these surfaces requires a slightly more involved effective potential
approach than the torus case due to the nonorthogonal coordinate grid necessary
to describe this problem. Amazingly this discussion allows one to very nicely
describe the geodesics of the surface of the more complicated ridged cavatappi
pasta.
