Prolate sheroidal coordinates can be used to simplify the Kepler problem in celestial mechanics. They are related to the usual Cartesian coordinates of Euclidean three-space by:
x=sinh(mu)sin(theta)cos(theta)
y=sinh(mu)sin(theta)sin(theta)
z=cosh(mu)cos(theta)
In the plane y=0, what is the coordinate transformation matrix d(x^mu)/d(x^v') relating (x,z) to (nu,theta)?