In the plane y0 what is the coordinate transformation, Physics

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In the plane y0 what is the coordinate transformation

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)?

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