Geodesics on a Circular Cylinder: Solving Ch6 Q6.4

[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??

 

[Kurdt]

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

 

[physics_fun]

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

 

[Kurdt]

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.

 

[physics_fun]

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

 

[Kurdt]

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