Register to reply

Geodesics on R^2

by Statis
Tags: geodesics
Share this thread:
Apr23-08, 08:16 PM
P: 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
Phys.Org News Partner Mathematics news on
Heat distributions help researchers to understand curved space
Professor quantifies how 'one thing leads to another'
Team announces construction of a formal computer-verified proof of the Kepler conjecture

Register to reply

Related Discussions
Let M be a three dimensional Riemannian Manifold that is compact . . . Differential Geometry 0
Inflectional geodesics ? Differential Geometry 3
Why is it that in general geodesics are paths of stationary character Introductory Physics Homework 2
Light geodesic path Special & General Relativity 8
About null and timelike geodesics General Physics 5