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.


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