Tangent-Sphere Coordinates
Tangent-SphereCoordinates
A coordinate system (mu,nu,psi) given by the coordinate transformation
and defined for mu>0, nu in (-infty,infty), and psi in [0,2pi). Surfaces of constant mu are given by the toroids
surface of constant nu by the spheres tangent to the xy-plane
and surfaces of constant psi by the half-planes
| tanpsi=y/x. |
(6)
|
The metric coefficients are
g_(xx) = [画像:1/((mu^2+nu^2)^2)]
(7)
g_(yy) = [画像:1/((mu^2+nu^2)^2)]
(8)
g_(zz) = [画像:(mu^2)/((mu^2+nu^2)^2).]
(9)
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References
Moon, P. and Spencer, D. E. "Tangent-Sphere Coordinate (mu,nu,psi)." Fig. 4.01 in Field Theory Handbook, Including Coordinate Systems, Differential Equations, and Their Solutions, 2nd ed. New York: Springer-Verlag, pp. 104-106, 1988.Referenced on Wolfram|Alpha
Tangent-Sphere CoordinatesCite this as:
Weisstein, Eric W. "Tangent-Sphere Coordinates." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Tangent-SphereCoordinates.html