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Two-dimensional orthogonal coordinate system
Parabolic coordinates are a two-dimensional orthogonal coordinate system in which the coordinate lines are confocal parabolas. A three-dimensional version
Parabolic_coordinates
Three-dimensional orthogonal coordinate system
parabolic cylindrical coordinates are a three-dimensional orthogonal coordinate system that results from projecting the two-dimensional parabolic coordinate
Parabolic cylindrical coordinates
Parabolic_cylindrical_coordinates
Topics referred to by the same term
cylindrical coordinates parabolic Möbius transformation Parabolic geometry (disambiguation) Parabolic spiral Parabolic line In advanced mathematics: Parabolic cylinder
Parabolic
Method for specifying point positions
occur as coordinate curves. For example, the coordinate curves of parabolic coordinates are parabolas. In three-dimensional space, if one coordinate is
Coordinate_system
Two-dimensional laminar boundary layer that forms on a semi-infinite plate
boundary layer equations are Parabolic partial differential equation, the natural coordinates for the problem is parabolic coordinates. The transformation from
Blasius_boundary_layer
Curve from a cone intersecting a plane
inconic Director circle Elliptic coordinate system Equidistant set Parabolic coordinates Quadratic function Spherical conic The empty set is included as
Conic_section
Vector used in astronomy
Hamilton–Jacobi equation is separable in both spherical coordinates and parabolic coordinates, as described below. Maximally superintegrable systems follow
Laplace–Runge–Lenz_vector
Plane curve: conic section
parabolas. The parabola has many important applications, from a parabolic antenna or parabolic microphone to automobile headlight reflectors and the design
Parabola
Reflector that has the shape of a paraboloid
associated adjective parabolic are often used in place of paraboloid and paraboloidal. If a parabola is positioned in Cartesian coordinates with its vertex
Parabolic_reflector
Three-dimensional orthogonal coordinate system
coordinates are three-dimensional orthogonal coordinates ( μ , ν , λ ) {\displaystyle (\mu ,\nu ,\lambda )} that generalize two-dimensional parabolic
Paraboloidal_coordinates
Method of solution for certain mechanical problems
Kepler problem is completely separable in both spherical coordinates and parabolic coordinates. Physics portal Bohr–Sommerfeld model Integrable system
Action-angle_coordinates
Coordinates comprising a distance and an angle
mathematician Blaise Pascal subsequently used polar coordinates to calculate the length of parabolic arcs. In Method of Fluxions (written 1671, published
Polar_coordinate_system
Type of antenna
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
Parabolic_antenna
Set of coordinates where the coordinate hypersurfaces all meet at right angles
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
Orthogonal_coordinates
Physical interaction of charged particles
wavefunction. These mathematical issues can be solved by applying parabolic coordinates leading to solutions in terms of confluent hypergeometric functions
Coulomb_scattering
Circulation density in a vector field
curvilinear orthogonal coordinates, e.g. in Cartesian coordinates, spherical, cylindrical, or even elliptical or parabolic coordinates: ( curl F ) 1 = 1
Curl_(mathematics)
Coordinate system in special relativity
particularly special relativity, light-cone coordinates, introduced by Paul Dirac and also known as Dirac coordinates, are a special coordinate system where
Light-cone_coordinates
Partial differential equations
cylindrical coordinates spherical coordinates Prolate spheroidal coordinates Oblate spheroidal coordinates Parabolic coordinates Toroidal coordinates Bispherical
Green's function for the three-variable Laplace equation
Green's_function_for_the_three-variable_Laplace_equation
Concept in mathematics
variables is used on Laplace's equation when expressed in parabolic cylindrical coordinates. The above equation may be brought into two distinct forms
Parabolic_cylinder_function
Approach to public-key cryptography
"projective coordinates" to refer to what is commonly called Jacobian coordinates. An additional speed-up is possible if mixed coordinates are used. Reduction
Elliptic-curve_cryptography
Three-dimensional solid
(parabola, ellipse, hyperbola) then the solid cylinder is said to be parabolic, elliptic and hyperbolic, respectively. For a right circular cylinder
Cylinder
One-dimensional complex manifold
Picard theorem: maps from hyperbolic to parabolic to elliptic are easy, but maps from elliptic to parabolic or parabolic to hyperbolic are very constrained
Riemann_surface
Limit of the tangent line at a point that tends to infinity
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
Asymptote
Indian physicist, educator and administrator
Degeneracy of the Hydrogen Atom and its Non-accidental Solution in Parabolic Coordinates". Canadian Journal of Physics. 99 (10): 853–860. Bibcode:2021CaJPh
Pranawachandra_Deshmukh
In physics, solution to Schrödinger equation
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
Coulomb_wave_function
Partial differential equation describing the evolution of temperature in a region
and physics (more specifically thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first
Heat_equation
Motion of launched objects due to gravity
air resistance neglected. In this idealized model, the object follows a parabolic path determined by its initial velocity and the constant acceleration
Projectile_motion
Kepler orbit with an eccentricity of less than one
orbit. Special cases with fewer degrees of freedom are the circular and parabolic orbit. Because at least six variables are absolutely required to completely
Elliptic_orbit
Rational function of the form (az + b)/(cz + d)
We first treat the non-parabolic case, for which there are two distinct fixed points. Non-parabolic case: Every non-parabolic transformation is conjugate
Möbius_transformation
System for specifying positions of celestial objects
celestial sphere, if the object's distance is unknown or trivial. Spherical coordinates, projected on the celestial sphere, are analogous to the geographic coordinate
Astronomical coordinate systems
Astronomical_coordinate_systems
Quantum effect in physics
electrostatic (DC) field was solved schematically by Lev Landau, using parabolic coordinates. This provides a simplified physical system that given it proper
Tunnel_ionization
Parameters that define a specific orbit
ellipse). This value is positive for elliptical orbits, undefined for parabolic trajectories, and negative for hyperbolic trajectories, which can hinder
Orbital_elements
Horizontal angle from north or other reference cardinal direction
coordinate system, used in celestial navigation, azimuth is one of the two coordinates. The other is altitude, sometimes called elevation above the horizon
Azimuth
bursting, parabolic bursting, and elliptic bursting), the theta model describes parabolic bursting, which is characterized by a parabolic frequency curve
Theta_model
Model compatible with special relativity
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
Relativistic_heat_conduction
Center of mass of multiple bodies orbiting each other
large distance between them. In astronomy, barycentric coordinates are non-rotating coordinates with the origin at the barycenter of two or more bodies
Barycenter_(astronomy)
Circles in two perpendicular families
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
Apollonian_circles
Cubic plane curve
found it as a caustic, the bright curve formed by light reflected in a parabolic mirror. It was used by Eugène Catalan in an angle trisection, and it appears
Tschirnhausen_cubic
Astrodynamic equation
an orbit that is a conic section (i.e. circular orbit, elliptic orbit, parabolic trajectory, hyperbolic trajectory, or radial trajectory) with the central
Orbit_equation
Concentrated solar thermal power station in the Mojave Desert of California
Map all coordinates using OpenStreetMap Download coordinates as: KML GPX (all coordinates) GPX (primary coordinates) GPX (secondary coordinates) Solar
Solar Energy Generating Systems
Solar_Energy_Generating_Systems
Apparent force in a rotating reference frame
of the fluid naturally assumes the correct parabolic shape. This fact may be exploited to make a parabolic turntable by using a fluid that sets after
Coriolis_force
Comets with a period of over 1,000 years
comets List of Halley-type comets List of long-period comets List of parabolic and hyperbolic comets List of Kreutz sungrazers J. A. Fernández; A. Sosa
List_of_near-parabolic_comets
Field of classical mechanics concerned with the motion of spacecraft
(1687), which gave a method for finding the orbit of a body following a parabolic path from three observations. This was used by Edmund Halley to establish
Orbital_mechanics
Solar thermal energy
in Asia. It uses a curved mirror, or an array of mirrors, acting as a parabolic reflector, which can reach temperatures of up to 3,000 degrees Celsius
Solar_furnace_of_Uzbekistan
Classical solution for inviscid, incompressible flow around a cylinder
-{\frac {a}{r}}\right)+\mathrm {O} \left(\varepsilon ^{2}\right)\,.} Here a parabolic shear in the outer velocity is introduced. ψ = U ( y + 1 6 ε y 3 a 2 )
Potential flow around a circular cylinder
Potential_flow_around_a_circular_cylinder
Class of partial differential equations
modeling, elliptic PDEs are frequently used to model steady states, unlike parabolic and hyperbolic PDEs, which generally model phenomena that change in time
Elliptic partial differential equation
Elliptic_partial_differential_equation
Overview of and topical guide to geometry
Noncommutative algebraic geometry Noncommutative geometry Ordered geometry Parabolic geometry Plane geometry Projective geometry Quantum geometry Riemannian
Outline_of_geometry
Simply connected Riemann surface is equivalent to an open disk, complex plane, or sphere
universal cover ("elliptic"), those with the plane as universal cover ("parabolic") and those with the unit disk as universal cover ("hyperbolic"). It further
Uniformization_theorem
Parametrizes complex structures on a surface
are represented by curves freely homotopic to a puncture are sent to parabolic elements of P S L 2 ( R ) {\displaystyle \mathrm {PSL} _{2}(\mathbb {R}
Teichmüller_space
Curved path of an object around a point
total energy, the parabolic trajectories zero total energy and hyperbolic orbits positive total energy. An open orbit will have a parabolic shape if it has
Orbit
Path of a moving object
mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete trajectory is defined by position and momentum, simultaneously
Trajectory
War monument in Tacna, Peru
the Heroes (Spanish: Monumento a los Héroes), popularly known as the Parabolic Arch (Spanish: Arco Parabólico), is a quarried pink stone monument located
Tacna_Parabolic_Arch
Plane fractal built from squares
that it satisfies the elliptic Harnack inequality without satisfying the parabolic one. The existence of such an example was an open problem for many years
Sierpiński_carpet
Map all coordinates using OpenStreetMap Download coordinates as: KML GPX (all coordinates) GPX (primary coordinates) GPX (secondary coordinates) Launch
List of Cape Canaveral and Merritt Island launch sites
List_of_Cape_Canaveral_and_Merritt_Island_launch_sites
Type of differential equation
topics, on which there is still much active research, include elliptic and parabolic partial differential equations, fluid mechanics, Boltzmann equations,
Partial_differential_equation
will be more and more elongated, and at e=1, the object's orbit will be parabolic and unbound to the Solar System (i.e. not returning for another orbit)
List of Solar System objects by greatest aphelion
List_of_Solar_System_objects_by_greatest_aphelion
Provincial park in Saskatchewan, Canada
Commons Map all coordinates using OpenStreetMap Download coordinates as: KML GPX (all coordinates) GPX (primary coordinates) GPX (secondary coordinates)
Athabasca Sand Dunes Provincial Park
Athabasca_Sand_Dunes_Provincial_Park
Technique for solving hyperbolic partial differential equations
in general characteristic curves can also be found for hyperbolic and parabolic partial differential equations. The method is to reduce a partial differential
Method_of_characteristics
Process of constructing a curve that has the best fit to a series of data points
influence of gravity follow a parabolic path, when air resistance is ignored. Hence, matching trajectory data points to a parabolic curve would make sense.
Curve_fitting
Mathematical space
complete as an algebraic variety. In particular, H {\displaystyle H} is a parabolic subgroup of G L ( V ) {\displaystyle \mathrm {GL} (V)} . Over R {\displaystyle
Grassmannian
Map all coordinates using OpenStreetMap Download coordinates as: KML GPX (all coordinates) GPX (primary coordinates) GPX (secondary coordinates) Renewable
List of solar thermal power stations
List_of_solar_thermal_power_stations
Differential operator in mathematics
variable. In other coordinate systems, such as cylindrical and spherical coordinates, the Laplacian also has a useful form. Informally, the Laplacian Δf (p)
Laplace_operator
Type of non-Euclidean geometry
the now rarely used sequence elliptic geometry (spherical geometry), parabolic geometry (Euclidean geometry), and hyperbolic geometry. In the former
Hyperbolic_geometry
Arch-monument in Kolkata, India
Minister of West Bengal, Mamata Banerjee. The ring is supported by two parabolic arches from four sides of the intersection. This gate is 55 metres (180
Biswa_Bangla_Gate
Product of the principal curvatures of a surface
= 0, the Gaussian curvature is zero and the surface is said to have a parabolic point. Most surfaces will contain regions of positive Gaussian curvature
Gaussian_curvature
Two geometries based on axioms closely related to those specifying Euclidean geometry
"hyperbolic" and "elliptic" (in his system he called Euclidean geometry parabolic, a term that generally fell out of use). His influence has led to the
Non-Euclidean_geometry
French and European spaceport in French Guiana
Map all coordinates using OpenStreetMap Download coordinates as: KML GPX (all coordinates) GPX (primary coordinates) GPX (secondary coordinates) The Guiana
Guiana_Space_Centre
Quantum chemistry rule regarding vibronic transitions
shapes. Equal spacing between vibrational levels is only the case for the parabolic potential of simple harmonic oscillators, in more realistic potentials
Franck–Condon_principle
Integer side lengths of a right triangle
narrow parabolic strip. For instance, 382 = 1444, 2 × 272 = 1458, 3 × 222 = 1452, 5 × 172 = 1445 and 10 × 122 = 1440; the corresponding parabolic strip
Pythagorean_triple
Orbit with a fixed distance from the barycenter
in a circular orbit) and the time to fall to a point mass in a radial parabolic orbit T par = 2 3 r 3 μ {\displaystyle T_{\text{par}}={\frac {\sqrt {2}}{3}}{\sqrt
Circular_orbit
Brazilian Space Center
Map all coordinates using OpenStreetMap Download coordinates as: KML GPX (all coordinates) GPX (primary coordinates) GPX (secondary coordinates) The Alcântara
Alcântara_Space_Center
Type of mathematical model
Mathematically, reaction–diffusion systems take the form of semi-linear parabolic partial differential equations. They can be represented in the general
Reaction–diffusion_system
Characteristic of conic sections
sections by eccentricity: Classification of elements of SL2(R) as elliptic, parabolic, and hyperbolic – and similarly for classification of elements of PSL2(R)
Eccentricity_(mathematics)
Curve used in computer graphics and related fields
number of steps in either direction can be read off from the endpoint coordinates; in for example the 0–45° sector horizontal movement to the right dominates
Bézier_curve
Map all coordinates using OpenStreetMap Download coordinates as: KML GPX (all coordinates) GPX (primary coordinates) GPX (secondary coordinates) Canada's
List of national parks of Canada
List_of_national_parks_of_Canada
Limiting set in dynamical systems
systems, the n dimensions may be, for example, two or three positional coordinates for each of one or more physical entities; in economic systems, they
Attractor
Country in West Asia
by the Futron's Space Competitiveness Index. The Israel Space Agency coordinates all space research programmes with scientific and commercial goals, and
Israel
Solar parabolic-trough component
Martin Next Generation Solar Energy Center is the solar parabolic-trough component of an integrated solar combined cycle (ISCC) 1150 MW plant, in western
Martin Next Generation Solar Energy Center
Martin_Next_Generation_Solar_Energy_Center
All points whose relative distances to two circles are same
y} -axis as common tangent. Such a system of circles is called coaxal parabolic circles (see below). b) Shrinking c 1 {\displaystyle c_{1}} to its center
Radical_axis
Office complex in downtown Toronto, Ontario, Canada
freestanding supports on each side of the Galleria, which branch out into parabolic shapes evoking a forest canopy or a tree-lined avenue because of the presence
Brookfield_Place_(Toronto)
Equations that describe the behavior of a physical system
acceleration Equations for a falling body Parabolic trajectory Curvilinear coordinates Orthogonal coordinates Newton's laws of motion Projectile motion
Equations_of_motion
Geometric inversion of a torus, cylinder or double cone
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
Dupin_cyclide
Bridge in NY, USA
The Hadley Parabolic Bridge, often referred to locally as the Hadley Bow Bridge, carries Corinth Road (Saratoga County Route 1) across the Sacandaga River
Hadley_Parabolic_Bridge
Celestial orbit whose trajectory is a conic section in the orbital plane
eccentricity. For a parabolic orbit, let e = 1 {\displaystyle e=1} and p = 2 f {\displaystyle p=2f} in (13) so that the orbit in polar coordinates is r = 2 f 1
Kepler_orbit
American space transportation venture
Birdzilla's Eye View of the Stratolaunch Hangar Under Construction". Parabolic Arc. Archived from the original on November 4, 2013. Retrieved November
Stratolaunch_Systems
Concentrating solar power plant
include 3 plants: Shams 1 became operational on 17 March 2013. Using parabolic trough technology with a capacity of 100 megawatts (MW), Shams 1 was the
Shams_Solar_Power_Station
Orbital mechanics term
). Barker's equation is used for parabolic trajectories (for which e = 1 {\displaystyle e=1} ). With the parabolic orbit, unlike the elliptical or hyperbolic
Kepler's_equation
Special orthogonal group
Polytope, 1905. Stringham, Irving (1901). "On the geometry of planes in a parabolic space of four dimensions". Transactions of the American Mathematical Society
Rotations in 4-dimensional Euclidean space
Rotations_in_4-dimensional_Euclidean_space
Equation for function that computes iterated values
solutions (Fatou coordinates) can be approximated by asymptotic expansion of a function defined by power series in the sectors around a parabolic fixed point
Abel_equation
Network of radio communication facilities run by NASA
section's coordinates using OpenStreetMap Download coordinates as: KML GPX (all coordinates) GPX (primary coordinates) GPX (secondary coordinates) DSN currently
NASA_Deep_Space_Network
Spiral that surrounds equal area per turn
A Fermat's spiral or parabolic spiral is a plane curve with the property that the area between any two consecutive full turns around the spiral is invariant
Fermat's_spiral
Overview of solar power in the U.S. state of Arizona
Solana Generating Station, a 280 MW parabolic trough solar plant, when commissioned in 2013, was the largest parabolic trough plant in the world and the
Solar_power_in_Arizona
House in Los Angeles, California
feet above the canyon below. Also known as the "Rainbow House" for its parabolic roof over stained glass windows and a curved ceiling that rises to 30
Garcia_House_(Los_Angeles)
Greek mathematician and physicist (c. 287 – 212 BC)
rotates with constant angular velocity. Equivalently, in modern polar coordinates (r, θ), it can be described by the equation r = a + b θ {\displaystyle
Archimedes
"Bouncing back" of waves at an interface
have optical power. Such mirrors may have surfaces that are spherical or parabolic. If the reflecting surface is very smooth, the reflection of light that
Reflection_(physics)
Curve formed by a hanging chain
It is often said that Galileo thought the curve of a hanging chain was parabolic. However, in his Two New Sciences (1638), Galileo wrote that a hanging
Catenary
Feature of a system that is preserved under some transformation
resistance) and then playing it back. The object will follow the same parabolic trajectory through the air, whether the recording is played normally or
Symmetry_(physics)
Bridge over the Susquehanna River in Binghamton, New York
South Washington Street Parabolic Bridge, originally known as the Washington Street Bridge, is a historic lenticular truss bridge located at Binghamton
South Washington Street Parabolic Bridge
South_Washington_Street_Parabolic_Bridge
Concentrated solar thermal power station in Spain
concentrated solar power station and Europe's first commercial plant to use parabolic troughs. It is located near Guadix in Andalusia, Spain, and its name is
Andasol_solar_power_station
Mansion in Barcelona designed by Gaudí
horse-drawn carriages through the front iron gates, which featured a parabolic arch and intricate patterns of forged ironwork resembling seaweed and
Palau_Güell
PARABOLIC COORDINATES
PARABOLIC COORDINATES
PARABOLIC COORDINATES
PARABOLIC COORDINATES
Girl/Female
American, Czech, Hindu, Indian
A Flower Name and Place Name
Boy/Male
Hindu, Indian, Traditional
The Eye of Visnu
Boy/Male
Hindu, Indian, Malayalam, Marathi
Royal Salute
Female
Greek
Variant spelling of Greek Aoide, AOEDE means "to sing."
Boy/Male
Tamil
Joyful
Girl/Female
British, English
Friend of the Elves
Boy/Male
Tamil
Gajhodhar | கஜà¯à®¹à¯‹à®¤à®¾à®°
Boy/Male
Hindu, Indian
The Greatest
Female
Egyptian
, a daughter of King Takelothes I.
Girl/Female
Muslim/Islamic
Turquoise
PARABOLIC COORDINATES
PARABOLIC COORDINATES
PARABOLIC COORDINATES
PARABOLIC COORDINATES
PARABOLIC COORDINATES
a.
Of the nature of a parable; expressed by a parable or figure; allegorical; as, parabolical instruction.
a.
Pertaining to, or designating, an acid derived from coal tar and other sources; as, carbolic acid (called also phenic acid, and phenol). See Phenol.
a.
Resembling a parabola in form.
a.
Alt. of Parabolical
a.
Generated by the revolution of a parabola, or by a line that moves on a parabola as a directing curve; as, a parabolic conoid.
a.
Of, pertaining to, or resembling, a paraboloid.
a.
Pertaining to, or designating, an organic acid metameric with malic acid.
n.
The solid generated by the rotation of a parabola about its axis; any surface of the second order whose sections by planes parallel to a given line are parabolas.
n.
One of a group of curves defined by the equation y = axn where n is a positive whole number or a positive fraction. For the cubical parabola n = 3; for the semicubical parabola n = /. See under Cubical, and Semicubical. The parabolas have infinite branches, but no rectilineal asymptotes.
a.
Pertaining to, or designating, an organic acid obtained as a deliquescent white crystalline substance, and isomeric with itaconic, citraconic, and mesaconic acids.
a.
Having the form or nature of a parabola; pertaining to, or resembling, a parabola; as, a parabolic curve.
adv.
By way of parable; in a parabolic manner.
adv.
In the form of a parabola.
a.
Alt. of Paragogical
n.
(Physiol.) A substance formed by a katabolic process; -- opposed to anastate. See Katabolic.
a.
Of or pertaining to katabolism; as, katabolic processes, which give rise to substances (katastates) of decreasing complexity and increasing stability.
a.
Pertaining to anabolism; an anabolic changes, or processes, more or less constructive in their nature.
n.
A solid formed by the revolution of a conic section about its axis; as, a parabolic conoid, elliptic conoid, etc.; -- more commonly called paraboloid, ellipsoid, etc.
v. t.
To apply carbolic acid to; to wash or treat with carbolic acid.
pl.
of Parabola