Problem 1

Derive equation (2.12) in Vallis (second edition):

$$\left(\frac{d\mathbf{V}_R}{dt}\right)_R = \left(\frac{d\mathbf{V}... ...\mathbf{V}_g - \boldsymbol{\Omega}\times(\boldsymbol{\Omega}\times\mathbf{r}) .$$