In green, confocal parabolae opening upwards, In red, confocal parabolae opening downwards,
Parabolic coordinates are a two-dimensional orthogonal coordinate system in which the coordinate lines are confocal parabolas. A three-dimensional version of parabolic coordinates is obtained by rotating the two-dimensional system about the symmetry axis of the parabolas.
Parabolic coordinates have found many applications, e.g., the treatment of the Stark effect and the potential theory of the edges.
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Paraboliccoordinates are a two-dimensional orthogonal coordinate system in which the coordinate lines are confocal parabolas. A three-dimensional version...
parabolic cylindrical coordinates are a three-dimensional orthogonal coordinate system that results from projecting the two-dimensional parabolic coordinate...
occur as coordinate curves. For example, the coordinate curves of paraboliccoordinates are parabolas. In three-dimensional space, if one coordinate is...
boundary layer equations are Parabolic partial differential equation, the natural coordinates for the problem is paraboliccoordinates.: 142 The transformation...
associated adjective parabolic are often used in place of paraboloid and paraboloidal. If a parabola is positioned in Cartesian coordinates with its vertex...
parabolas. The parabola has many important applications, from a parabolic antenna or parabolic microphone to automobile headlight reflectors and the design...
A parabolic antenna is an antenna that uses a parabolic reflector, a curved surface with the cross-sectional shape of a parabola, to direct the radio...
inconic Director circle Elliptic coordinate system Equidistant set Paraboliccoordinates Quadratic function Spherical conic The empty set is included as...
In mathematics, orthogonal coordinates are defined as a set of d coordinates q = ( q 1 , q 2 , … , q d ) {\displaystyle \mathbf {q} =(q^{1},q^{2},\dots...
of parabolic arcs. In Method of Fluxions (written 1671, published 1736), Sir Isaac Newton examined the transformations between polar coordinates, which...
variables is used on Laplace's equation when expressed in parabolic cylindrical coordinates. The above equation may be brought into two distinct forms...
(parabola, ellipse, hyperbola) then the solid cylinder is said to be parabolic, elliptic and hyperbolic, respectively. For a right circular cylinder...
the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity. In projective geometry and related contexts, an asymptote...
celestial sphere, if the object's distance is unknown or trivial. Spherical coordinates, projected on the celestial sphere, are analogous to the geographic coordinate...
Coulomb wave function, can be found by solving this equation in paraboliccoordinates ξ = r + r → ⋅ k ^ , ζ = r − r → ⋅ k ^ ( k ^ = k → / k ) . {\displaystyle...
electrostatic (DC) field was solved schematically by Lev Landau, using paraboliccoordinates. This provides a simplified physical system that given it proper...
Picard theorem: maps from hyperbolic to parabolic to elliptic are easy, but maps from elliptic to parabolic or parabolic to hyperbolic are very constrained...
CVT, a type of continuously variable transmission Toroidal reflector, a parabolic reflector which has a different focal distance depending on the angle...
pencil is another hyperbolic pencil, and the inversion of a parabolic pencil is another parabolic pencil. It is relatively easy to show using inversion that...
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