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.