|Apr23-08, 08:16 PM||#1|
Geodesics on R^2
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 ?
|Similar Threads for: Geodesics on R^2|
|Let M be a three dimensional Riemannian Manifold that is compact . . .||Differential Geometry||0|
|Inflectional geodesics ?||Differential Geometry||3|
|Geodesics||Introductory Physics Homework||2|
|geodesics||Special & General Relativity||8|
|about null and timelike geodesics||General Physics||5|