# Bipolar toroidal coordinates - position vector, velocity and acceleration

Bipolar toroidal coordinates:

$x = a \frac{\sinh\tau \cos\phi}{\cosh\tau-\cos\sigma}$

$y = a \frac{\sinh\tau \sin\phi}{\cosh\tau-\cos\sigma}$

$z=a \frac{\sin\sigma}{\cosh\tau-\cos\sigma}$

Would anyone know the expressions for position vector ${\mathbf r}$, velocity $\dot{\mathbf r}$ and acceleration $\ddot{\mathbf r}$ in these coordinates.