Hi, i'm working on marionþton ch6 question 6.4. "Show that the geodesic on the surface of a straight circular cylinder is a (partial) helix" I used the example of the geodesic on a sphere in the book, but when i calculate the angle phi i get something like phi=b*z+c, where b and c are constants; this is a straight line?! Or does it just mean that the 'speed' of phi doesn't change in time??
I still don't think you got what I meant. The equation you came up with shows a linear change in phi with z. Now imagine a cylinder that has a line drawn on its inside surface that changes linearly by 2pi over the total length z. The line drawn on the inside would be part of a helix. Just making sure you can visualise that.