Geodesic
Orthogonal Curvilinear Coordinate Systems Corresponding to Singular Spectral Curves
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 180-196

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We study the limiting case of the Krichever construction of orthogonal curvilinear coordinate systems when the spectral curve becomes singular. We show that when the curve is reducible and all its irreducible components are rational curves, the construction procedure reduces to solving systems of linear equations and to simple computations with elementary functions. We also demonstrate how well-known coordinate systems, such as polar coordinates, cylindrical coordinates, and spherical coordinates in Euclidean spaces, fit in this scheme. 
@article{TM_2006_255_a13,
     author = {A. E. Mironov and I. A. Taimanov},
     title = {Orthogonal {Curvilinear} {Coordinate} {Systems} {Corresponding} to {Singular} {Spectral} {Curves}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {180--196},
     publisher = {mathdoc},
     volume = {255},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2006_255_a13/}
}
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A. E. Mironov; I. A. Taimanov. Orthogonal Curvilinear Coordinate Systems Corresponding to Singular Spectral Curves. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 180-196. http://geodesic.mathdoc.fr/item/TM_2006_255_a13/