Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Geodesics on R^2

  1. Apr 23, 2008 #1

    Suppose that [tex]R^2[/tex] is provided with the following metric

    ds^2 = dx^2 + (\cosh(x))^2 dy^2
    Can we find a general exact formula [tex]\alpha(t)[/tex] for the geodesics (starting at an arbitrary point) ?

    The geodesic equation gives
    x'' - \cosh(x)\sinh(x) (y')^2 = 0
    y'' + 2 \tanh(x) x' y' = 0

    I guess that since this model is simply a reparametrization of the Hyperbolic space on R^2 the geodesics should be known ?

    Thank you
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Threads - Geodesics Date
Geodesic dome angles Sep 22, 2010
Geodesic distance on Earth Aug 8, 2006