Question

@ganeshie8

Answer 1

Show that the geodesic on the surface of a right circular cylinder is a segment of a helix.

Answer 2

I guess this one also requires Euler's equation

Answer 3

should we be using cylindrical coordinates for arc length integral ?

Answer 4

Yeah, that sounds about right

Answer 5

I'm not exactly sure how the figure would look for this?

Answer 6

yeah since the radius is constant, lets try and express ds in terms of \(z\) and \(\theta\)

Answer 7

Ok, so lets start with our distance along the surface which is \[dS = \sqrt{dx^2+dy^2+dz^2}\] and now we can set it up using spherical coordinates as you suggested

Answer 8

Err cylindrical, I was thinking spherical