- #1
gboff21
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Homework Statement
The metric for this surface is [itex]ds^2 = dr^2 + r^2\omega^2d\phi^2[/itex], where [itex]\omega = sin(\theta_0)[/itex].
Solve the Euler-Lagrange equation for phi to show that [itex]\dot{\phi} = \frac{k}{\omega^2r^2}[/itex]. Then sub back into the metric to get [itex]\dot{r}[/itex]
Homework Equations
[itex]L = 1/2 g_{ab} \dot{x}^a \dot{x}^b[/itex]
The Attempt at a Solution
I've solved it to get [itex]\ddot{\phi} + 2\frac{\dot{r}}{r}\dot{\phi} = 0 [/itex]
and
[itex]\ddot{r} - r\omega^2\dot{\phi}^2 = 0[/itex]
So how on Earth do you get that answer?