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ehrenfest
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Homework Statement
I am trying to find a geodesic with Euler-Lagrange equation by varying the function
[tex] ds/d\tau = \sqrt{\dot{x} + \dot{y}} [/tex]
EDIT: it should be [tex] ds/d\tau = \sqrt{\dot{x}^2 + \dot{y}^2} [/tex]
where tau is a parametrization and the dot means a tau derivative.
However, when I plug that into the EL equation for either x or y, I get:
[tex] (\dot{x} + \dot{y})^{3/2}(\ddot{x}+\ddot{y})=0 [/tex]
How do I get a line from that?
Homework Equations
The Attempt at a Solution
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