Coordinate System - 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

Read more about this topic:  Coordinate System

Other articles related to "list of orthogonal coordinate systems, orthogonal, coordinate systems, orthogonal coordinate systems, coordinate, coordinate system, coordinates":

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 ...
Classical Group - Relationship With Bilinear Forms
... 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 ... to drop the condition that the determinant be 1 and consider unitary groups and (disconnected) orthogonal groups ...
Cubes - Orthogonal Projections
... The cube has four special orthogonal projections, centered, on a vertex, edges, face and normal to its vertex figure ... Orthogonal projections Centered by Face Vertex Coxeter planes B2 A2 Projective symmetry Tilted views ...
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 appears that is a Padé approximation ... the density ρ an effective measure for transforming the secondary polynomials into an orthogonal system ...
Lauricella's Theorem
... In the theory of orthogonal functions, Lauricella's theorem provides a condition for checking the closure of a set of orthogonal functions, namely Theorem ... A necessary and sufficient condition that a normal orthogonal set be closed is that the formal series for each function of a known closed normal orthogonal set in terms of converge in the mean to that function ...

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