# Geodesic Equation

1. Aug 16, 2015

### peterpang1994

As the geodesic equation in a form of

is quite familiar for me. But I still cannot derive it in terms of time coordinate parameter;

I can't get the second term on the right hand side
what I can get is
½{d[lngαβ(dxα/dt)(dxβ/dt)]/dt}dxμ/dt

How can I obtain that term?

2. Aug 16, 2015

### Orodruin

Staff Emeritus
I suggest you do not work in terms of the metric. The equation follows directly from the variable substitution to parameterise the curve with $t$ instead of $s$ and looking at how the geodesic equation transforms under this change. Keep in mind that
$$\frac{d^2 t}{ds^2} = - \Gamma^0_{\alpha\beta} \dot x^\alpha \dot x^\beta .$$