How Do You Derive the Geodesic Equation?

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The discussion focuses on deriving the geodesic equation from the provided equations in flat space. The user expresses confusion about how to combine the equations effectively and seeks clarification on making the equation covariant. Key points include the definition of a straight line in flat space and the relationship between the derivatives of the coordinates. Participants emphasize the importance of understanding the underlying principles of differential geometry to approach the derivation. The conversation aims to clarify the steps needed to achieve a clear understanding of the geodesic equation.
PhysicistFTW
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1. A straight line in flat space may be defined by the equation:
(when I use the ^ symbol in this case it means like upper subscript not to the power)


(U^v)(d/dx^v)(U^u)=0


(U^u=dx^u/ds)

derive the geodesic equation.

Please help I'm completely clueless all I can really see to do is mix the two equations but that doesn't really show me anything more clearly, any help would be greatly appreciated.


 
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also it says to make the equation covariant if that helps
 

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