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Geodesic in cylinder 
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#1
Sep706, 02:02 AM

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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?? 


#2
Sep706, 05:59 AM

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



#3
Sep706, 06:35 AM

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


#4
Sep806, 05:10 AM

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Geodesic in cylinder
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
Sep1106, 04:02 AM

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



#6
Sep1106, 04:36 AM

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



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