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## Homework Statement

Below: Jac = Jacobian matrix; ξ = d/dφ for some continuous parameter φ which labels different points on the worldline.

(I'm sorry for my poor English.)

Consider a new coordinate system x

^{µ'}which differs from the original Cartesian coordinate system x

^{µ}; the Cartesian coordinates x

^{µ}can be written as a function of these new coordinates x

^{µ}= x

^{µ}(x

^{µ'}). Show that the equation of motion can be written in these new x

^{µ'}coordinates as ξ²x

^{µ'}+ Γ

^{µ'}

_{ν'}

_{λ'}ξx

^{ν'}ξx

^{λ'}= 0 for some Γ

^{µ}'

_{ν'}

_{λ'}which you must compute; Γ

^{µ'}

_{ν'}

_{λ'}is known as the Christoffel symbol. These extra Christoffel terms in the equation of motion can be thought of as ”fictitous forces” that arise in an accelerated reference frame.

## Homework Equations

x

^{µ'}= Jac * x

^{µ}

## The Attempt at a Solution

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I've tried to solve this by deriving x

^{µ'}with respect to φ using the chain rule, but that did not work. Unfortunately I could not put my work here, but it was just what I said: I've used the chain rule to derive x

^{µ'}with respect to φ.