Acceleration in a new Coordinate System - General Relativity

[kent davidge]

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.

 

[Asim Riaz]

I've tried to look up how to solve this but I could not find anything. It would be really nice if someone can help me out.