parabolic cylinders. Parabolic cylindrical coordinates have found many applications, e.g., the potential theory of edges. The parabolic cylindrical coordinates...

Parabolic coordinates are a two-dimensional orthogonal coordinate system in which the coordinate lines are confocal parabolas. A three-dimensional version...

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

parable. Parabolic may refer to: In mathematics: In elementary mathematics, especially elementary geometry: Parabolic coordinates Parabolic cylindrical coordinates...

complete solution for S {\displaystyle S} . The Hamiltonian in parabolic cylindrical coordinates can be written H = p σ 2 + p τ 2 2 m ( σ 2 + τ 2 ) + p z 2...

an element of the cylindrical surface. A solid bounded by a cylindrical surface and two parallel planes is called a (solid) cylinder. The line segments...

parabolic coordinates. They possess elliptic paraboloids as one-coordinate surfaces. As such, they should be distinguished from parabolic cylindrical coordinates...

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...

 θ, z). Spherical coordinates take this a step further by converting the pair of cylindrical coordinates (r, z) to polar coordinates (ρ, φ) giving a triple...

Cartesian coordinates, one has to solve a (difficult) two dimensional boundary value problem involving a partial differential equation, but in cylindrical coordinates...

cone, parabolic cylinder, elliptical paraboloid, hyperbolic paraboloid, hyperboloid of one sheet, hyperboloid of two sheets. Elliptic cone Parabolic cylinder...

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

In polar coordinates, Laplace's equation is (see Del in cylindrical and spherical coordinates): 1 r ∂ ∂ r ( r ∂ ϕ ∂ r ) + 1 r 2 ∂ 2 ϕ ∂ θ 2 = 0 . {\displaystyle...

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

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

complex plane, which is parabolic. With two punctures, it is the punctured plane or alternatively annulus or cylinder, which is parabolic. With three or more...

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

meridian. In mathematics, the azimuth angle of a point in cylindrical coordinates or spherical coordinates is the anticlockwise angle between the positive x-axis...

in a Newtonian context is modelled by the Fourier equation, namely a parabolic partial differential equation of the kind: ∂ θ ∂ t   =   α   ∇ 2 θ , {\displaystyle...

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

authors believed he might have used mirrors acting collectively as a parabolic reflector to burn ships attacking Syracuse. Lucian wrote, in the second...

first case one defines the cyclide as elliptic, in the second case as parabolic. In both cases the conics are contained in two mutually orthogonal planes...

telescope is a 530-metre (1,740 ft) long and 30-metre (98 ft) tall cylindrical parabolic antenna. It operates at a frequency of 326.5 MHz with a maximum...

the concept of leakage. Another useful coordinate system is 3D cylindrical coordinates (typically where a pumping well is a line source located at the...

Navier–Stokes equations in cylindrical coordinates, retrieved 2016-12-26 Eric W. Weisstein (2005-10-26), Spherical Coordinates, MathWorld, retrieved 2008-01-22...

in a cylindrical vessel and is rotating around a vertical axis coinciding with the axis of the cylinder, the free surface will assume a parabolic surface...

polar configuration. Cylindrical near-field ranges measure the electric field on a cylindrical surface close to the AUT. Cylindrical harmonics are used...

antenna is comparable to a dish antenna, but uses the lens rather than a parabolic reflector as the main focusing element. As with the dish antenna, a feed...

vectors change as the coordinates change. These terms arise automatically on transformation to polar (or cylindrical) coordinates and are thus not fictitious...

can be solved in cylindrical coordinates ( r , θ , z ) {\displaystyle (r,\theta ,z)} . Denote the radii of the inner and outer cylinders as R 1 {\displaystyle...