1. Nov 10, 2011 #1

   Identity

   

   In Euclidean three-space with coordinates [itex](x,y,z)[/itex] and line element
   
   [tex]ds^2 = dx^2+dy^2-dz^2[/tex]
   
   It is easy to show using the geodesic equation that:
   
   [itex]x = lu+l'[/itex], [itex]y=mu+m'[/itex], [itex]z=nu+n'[/itex]
   
   where [itex]u[/itex] is an affine parameter.
   
   However, is it possible to find a relation between [itex]l,m,n[/itex]?

    

   Last edited: Nov 10, 2011

   Identity, Nov 10, 2011
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3. Nov 10, 2011 #2

   pervect

   

   Staff Emeritus

   Science Advisor

   Insights Author

   Shouldn't l,m, and n be analogous to a four-velocity in Minowskian space, and hence have a constant norm?

    

   pervect, Nov 10, 2011

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