Parabolic coordinates 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...

cylindrical coordinates parabolic Möbius transformation Parabolic geometry (disambiguation) Parabolic spiral Parabolic line In advanced mathematics: Parabolic cylinder...

boundary layer equations are Parabolic partial differential equation, the natural coordinates for the problem is parabolic coordinates.: 142  The transformation...

occur as coordinate curves. For example, the coordinate curves of parabolic coordinates are parabolas. In three-dimensional space, if one coordinate is...

inconic Director circle Elliptic coordinate system Equidistant set Parabolic coordinates Quadratic function Spherical conic The empty set is included as...

Hamilton–Jacobi equation is separable in both spherical coordinates and parabolic coordinates, as described below. Maximally superintegrable systems follow...

parabolas. The parabola has many important applications, from a parabolic antenna or parabolic microphone to automobile headlight reflectors and the design...

coordinates are three-dimensional orthogonal coordinates ( μ , ν , λ ) {\displaystyle (\mu ,\nu ,\lambda )} that generalize two-dimensional parabolic...

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...

of parabolic arcs. In Method of Fluxions (written 1671, published 1736), Sir Isaac Newton examined the transformations between polar coordinates, which...

Kepler problem is completely separable in both spherical coordinates and parabolic coordinates. Physics portal Bohr–Sommerfeld model Integrable system...

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...

curvilinear orthogonal coordinates, e.g. in Cartesian coordinates, spherical, cylindrical, or even elliptical or parabolic coordinates: ( curl ⁡ F ) 1 = 1...

associated adjective parabolic are often used in place of paraboloid and paraboloidal. If a parabola is positioned in Cartesian coordinates with its vertex...

wavefunction. These mathematical issues can be solved by applying parabolic coordinates leading to solutions in terms of confluent hypergeometric functions...

cylindrical coordinates spherical coordinates Prolate spheroidal coordinates Oblate spheroidal coordinates Parabolic coordinates Toroidal coordinates Bispherical...

"projective coordinates" to refer to what is commonly called Jacobian coordinates. An additional speed-up is possible if mixed coordinates are used. Reduction...

(parabola, ellipse, hyperbola) then the solid cylinder is said to be parabolic, elliptic and hyperbolic, respectively. For a right circular cylinder...

Coulomb wave function, can be found by solving this equation in parabolic coordinates ξ = r + r → ⋅ k ^ , ζ = r − r → ⋅ k ^ ( k ^ = k → / k ) . {\displaystyle...

particularly special relativity, light-cone coordinates, introduced by Paul Dirac and also known as Dirac coordinates, are a special coordinate system where...

actual orbit of these comets significantly differs from the provided coordinates. A Solar System barycentric orbit computed at an epoch when the object...

Picard theorem: maps from hyperbolic to parabolic to elliptic are easy, but maps from elliptic to parabolic or parabolic to hyperbolic are very constrained...

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...

variables is used on Laplace's equation when expressed in parabolic cylindrical coordinates. The above equation may be brought into two distinct forms...

electrostatic (DC) field was solved schematically by Lev Landau, using parabolic coordinates. This provides a simplified physical system that given it proper...

ellipse). This value is positive for elliptical orbits, infinity for parabolic trajectories, and negative for hyperbolic trajectories, which can hinder...

We first treat the non-parabolic case, for which there are two distinct fixed points. Non-parabolic case: Every non-parabolic transformation is conjugate...

orbit. Special cases with fewer degrees of freedom are the circular and parabolic orbit. Because at least six variables are absolutely required to completely...

In mathematics and physics, the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph...