Geodesic in cylinder

1. Sep 7, 2006

physics_fun

Hi, i'm working on marion&thornton 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??

2. Sep 7, 2006

Kurdt

Staff Emeritus
Phi changes linearly with z. Think about the implications of this.

3. Sep 7, 2006

physics_fun

That implies the equation should be linear....and it is!
Thanks!

4. Sep 8, 2006

Kurdt

Staff Emeritus
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.

5. Sep 11, 2006

physics_fun

I think that's just what I meant to say (my English is not always very good...)

6. Sep 11, 2006

Kurdt

Staff Emeritus
No problem. English is my first language and I struggle to express myself

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