Coord - List of Orthogonal Coordinate Systems

List of Orthogonal Coordinate Systems

In mathematics, two vectors are orthogonal if they are perpendicular. The following coordinate systems all have the properties of being orthogonal coordinate systems, that is the coordinate surfaces meet at right angles.

Orthogonal coordinate systems
Two dimensional orthogonal coordinate systems
  • Cartesian coordinate system
  • Polar coordinate system
  • Parabolic coordinate system
  • Bipolar coordinates
  • Hyperbolic coordinates
  • Elliptic coordinates
Three dimensional orthogonal coordinate systems
  • Cartesian coordinate system
  • Cylindrical coordinate system
  • Spherical coordinate system
  • Parabolic cylindrical coordinates
  • Paraboloidal coordinates
  • Oblate spheroidal coordinates
  • Prolate spheroidal coordinates
  • Ellipsoidal coordinates
  • Elliptic cylindrical coordinates
  • Toroidal coordinates
  • Bispherical coordinates
  • Bipolar cylindrical coordinates
  • Conical coordinates
  • Flat-ring cyclide coordinates
  • Flat-disk cyclide coordinates
  • Bi-cyclide coordinates
  • Cap-cyclide coordinates
  • Concave bi-sinusoidal single-centered coordinates
  • Concave bi-sinusoidal double-centered coordinates
  • Convex inverted-sinusoidal spherically aligned coordinates
  • Quasi-random-intersection cartesian coordinates

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... Bn = SO(2n + 1), the special orthogonal group of orthogonal (2n + 1)-by-(2n + 1) real matrices with determinant 1 ... Dn = SO(2n), the special orthogonal group of orthogonal 2n-by-2n real matrices with determinant 1 ... the condition that the determinant be 1 and consider unitary groups and (disconnected) orthogonal groups ...
Lauricella's Theorem
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Stieltjes Transformation - Relationships To Orthogonal Polynomials
... If {Pn} is a sequence of orthogonal polynomials for this product, we can create the sequence of associated secondary polynomials by the formula It ... from the density ρ an effective measure for transforming the secondary polynomials into an orthogonal system ...

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