Geodesics on a Circular Cylinder: Solving Ch6 Q6.4

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Homework Help Overview

The discussion revolves around a problem from Marion & Thornton concerning geodesics on the surface of a circular cylinder, specifically demonstrating that these geodesics can be represented as a helix. Participants are exploring the implications of their calculations related to the angle phi and its relationship with the vertical coordinate z.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the linear relationship between phi and z, questioning whether this indicates a straight line or a helical path. There is an exploration of visualizing the geometric implications of this relationship on the cylinder's surface.

Discussion Status

The discussion is active, with participants clarifying their understanding of the relationship between the variables involved. Some guidance has been offered regarding visualizing the helix on the cylinder, and there appears to be a productive exchange of ideas, although not all participants agree on the interpretation of the calculations.

Contextual Notes

Participants mention language barriers that may affect communication and understanding of the concepts being discussed.

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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??
 
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Phi changes linearly with z. Think about the implications of this.
 
That implies the equation should be linear...and it is!
Thanks!:smile:
 
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.
 
I think that's just what I meant to say (my English is not always very good...):smile:
 
No problem. English is my first language and I struggle to express myself :wink:
 

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