Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Free
Faster access than browser!
 

Spherical coordinate system

Index Spherical coordinate system

In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane. [1]

82 relations: Aircraft principal axes, Altitude, Astronomical object, Atan2, Azimuth, Cartesian coordinate system, Celestial coordinate system, Clockwise, Colatitude, Coordinate system, Curl (mathematics), Cylindrical coordinate system, Degree (angle), Del, Del in cylindrical and spherical coordinates, Differential (infinitesimal), Dimension, Divergence, Earth, Ecliptic coordinate system, Elevation (ballistics), Equator, Eric W. Weisstein, Euclidean distance, Euclidean vector, Euler angles, Fundamental plane (spherical coordinates), Galactic coordinate system, Geographic coordinate system, Gimbal lock, Gradient, Helmholtz equation, Henry Margenau, Herman Feshbach, Horizontal coordinate system, Hypersphere, IERS Reference Meridian, International Organization for Standardization, Interval (mathematics), ISO 31-11, ISO 80000-2, Jacobian matrix and determinant, Laplace operator, Laplace's equation, Latitude, Line element, Linear algebra, List of common coordinate transformations, Longitude, Loudspeaker, ..., Mathematics, MathWorld, Meridian (geography), Milky Way, Multiple integral, North, Partial differential equation, Phi, Philip M. Morse, Polar coordinate system, Position (vector), Prime meridian, Projection (linear algebra), Radian, Rho, Right-hand rule, Rotation around a fixed axis, Rotation matrix, Sea level, Separation of variables, Solid angle, Sphere, Spherical harmonics, Sun, Theodolite, Theta, Unit vector, Vector fields in cylindrical and spherical coordinates, Video game development, Volume element, World Geodetic System, Zenith. Expand index (32 more) »

Aircraft principal axes

An aircraft in flight is free to rotate in three dimensions: yaw, nose left or right about an axis running up and down; pitch, nose up or down about an axis running from wing to wing; and roll, rotation about an axis running from nose to tail.

New!!: Spherical coordinate system and Aircraft principal axes · See more »

Altitude

Altitude or height (sometimes known as depth) is defined based on the context in which it is used (aviation, geometry, geographical survey, sport, atmospheric pressure, and many more).

New!!: Spherical coordinate system and Altitude · See more »

Astronomical object

An astronomical object or celestial object is a naturally occurring physical entity, association, or structure that exists in the observable universe.

New!!: Spherical coordinate system and Astronomical object · See more »

Atan2

The function \operatorname (y,x) or \operatorname (y,x) is defined as the angle in the Euclidean plane, given in rad, between the positive x-axis and the ray to the Points in the upper half-plane deliver values in points with.

New!!: Spherical coordinate system and Atan2 · See more »

Azimuth

An azimuth (from the pl. form of the Arabic noun "السَّمْت" as-samt, meaning "the direction") is an angular measurement in a spherical coordinate system.

New!!: Spherical coordinate system and Azimuth · See more »

Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

New!!: Spherical coordinate system and Cartesian coordinate system · See more »

Celestial coordinate system

In astronomy, a celestial coordinate system is a system for specifying positions of celestial objects: satellites, planets, stars, galaxies, and so on.

New!!: Spherical coordinate system and Celestial coordinate system · See more »

Clockwise

Two-dimensional rotation can occur in two possible directions.

New!!: Spherical coordinate system and Clockwise · See more »

Colatitude

In spherical coordinates, colatitude is the complementary angle of the latitude, i.e. the difference between 90° and the latitude, where southern latitudes are denoted with a minus sign.

New!!: Spherical coordinate system and Colatitude · See more »

Coordinate system

In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

New!!: Spherical coordinate system and Coordinate system · See more »

Curl (mathematics)

In vector calculus, the curl is a vector operator that describes the infinitesimal rotation of a vector field in three-dimensional Euclidean space.

New!!: Spherical coordinate system and Curl (mathematics) · See more »

Cylindrical coordinate system

A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis, the direction from the axis relative to a chosen reference direction, and the distance from a chosen reference plane perpendicular to the axis.

New!!: Spherical coordinate system and Cylindrical coordinate system · See more »

Degree (angle)

A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360 degrees.

New!!: Spherical coordinate system and Degree (angle) · See more »

Del

Del, or nabla, is an operator used in mathematics, in particular in vector calculus, as a vector differential operator, usually represented by the nabla symbol ∇.

New!!: Spherical coordinate system and Del · See more »

Del in cylindrical and spherical coordinates

This is a list of some vector calculus formulae for working with common curvilinear coordinate systems.

New!!: Spherical coordinate system and Del in cylindrical and spherical coordinates · See more »

Differential (infinitesimal)

The term differential is used in calculus to refer to an infinitesimal (infinitely small) change in some varying quantity.

New!!: Spherical coordinate system and Differential (infinitesimal) · See more »

Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

New!!: Spherical coordinate system and Dimension · See more »

Divergence

In vector calculus, divergence is a vector operator that produces a scalar field, giving the quantity of a vector field's source at each point.

New!!: Spherical coordinate system and Divergence · See more »

Earth

Earth is the third planet from the Sun and the only astronomical object known to harbor life.

New!!: Spherical coordinate system and Earth · See more »

Ecliptic coordinate system

The ecliptic coordinate system is a celestial coordinate system commonly used for representing the apparent positions and orbits of Solar System objects.

New!!: Spherical coordinate system and Ecliptic coordinate system · See more »

Elevation (ballistics)

In ballistics, the elevation is the angle between the horizontal plane and the axial direction of the barrel of a gun, mortar or heavy artillery.

New!!: Spherical coordinate system and Elevation (ballistics) · See more »

Equator

An equator of a rotating spheroid (such as a planet) is its zeroth circle of latitude (parallel).

New!!: Spherical coordinate system and Equator · See more »

Eric W. Weisstein

Eric Wolfgang Weisstein (born March 18, 1969) is an encyclopedist who created and maintains MathWorld and Eric Weisstein's World of Science (ScienceWorld).

New!!: Spherical coordinate system and Eric W. Weisstein · See more »

Euclidean distance

In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space.

New!!: Spherical coordinate system and Euclidean distance · See more »

Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.

New!!: Spherical coordinate system and Euclidean vector · See more »

Euler angles

The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system.

New!!: Spherical coordinate system and Euler angles · See more »

Fundamental plane (spherical coordinates)

The fundamental plane in a spherical coordinate system is a plane of reference that divides the sphere into two hemispheres.

New!!: Spherical coordinate system and Fundamental plane (spherical coordinates) · See more »

Galactic coordinate system

The galactic coordinate system is a celestial coordinate system in spherical coordinates, with the Sun as its center, the primary direction aligned with the approximate center of the Milky Way galaxy, and the fundamental plane parallel to an approximation of the galactic plane but offset to its north.

New!!: Spherical coordinate system and Galactic coordinate system · See more »

Geographic coordinate system

A geographic coordinate system is a coordinate system used in geography that enables every location on Earth to be specified by a set of numbers, letters or symbols.

New!!: Spherical coordinate system and Geographic coordinate system · See more »

Gimbal lock

Gimbal lock is the loss of one degree of freedom in a three-dimensional, three-gimbal mechanism that occurs when the axes of two of the three gimbals are driven into a parallel configuration, "locking" the system into rotation in a degenerate two-dimensional space.

New!!: Spherical coordinate system and Gimbal lock · See more »

Gradient

In mathematics, the gradient is a multi-variable generalization of the derivative.

New!!: Spherical coordinate system and Gradient · See more »

Helmholtz equation

In mathematics & physics, the Helmholtz equation, named for Hermann von Helmholtz, is the partial differential equation where ∇2 is the Laplacian, k is the wavenumber, and A is the amplitude.

New!!: Spherical coordinate system and Helmholtz equation · See more »

Henry Margenau

Henry Margenau (April 30, 1901 – February 8, 1997) was a German-American physicist, and philosopher of science.

New!!: Spherical coordinate system and Henry Margenau · See more »

Herman Feshbach

Herman Feshbach (February 2, 1917, in New York City – 22 December, 2000, in Cambridge, Massachusetts) was an American physicist.

New!!: Spherical coordinate system and Herman Feshbach · See more »

Horizontal coordinate system

The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane.

New!!: Spherical coordinate system and Horizontal coordinate system · See more »

Hypersphere

In geometry of higher dimensions, a hypersphere is the set of points at a constant distance from a given point called its center.

New!!: Spherical coordinate system and Hypersphere · See more »

IERS Reference Meridian

The IERS Reference Meridian (IRM), also called the International Reference Meridian, is the prime meridian (0° longitude) maintained by the International Earth Rotation and Reference Systems Service (IERS).

New!!: Spherical coordinate system and IERS Reference Meridian · See more »

International Organization for Standardization

The International Organization for Standardization (ISO) is an international standard-setting body composed of representatives from various national standards organizations.

New!!: Spherical coordinate system and International Organization for Standardization · See more »

Interval (mathematics)

In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.

New!!: Spherical coordinate system and Interval (mathematics) · See more »

ISO 31-11

ISO 31-11:1992 was the part of international standard ISO 31 that defines mathematical signs and symbols for use in physical sciences and technology.

New!!: Spherical coordinate system and ISO 31-11 · See more »

ISO 80000-2

ISO 80000-2:2009 is a standard describing mathematical signs and symbols developed by the International Organization for Standardization (ISO), superseding ISO 31-11.

New!!: Spherical coordinate system and ISO 80000-2 · See more »

Jacobian matrix and determinant

In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.

New!!: Spherical coordinate system and Jacobian matrix and determinant · See more »

Laplace operator

In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space.

New!!: Spherical coordinate system and Laplace operator · See more »

Laplace's equation

In mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties.

New!!: Spherical coordinate system and Laplace's equation · See more »

Latitude

In geography, latitude is a geographic coordinate that specifies the north–south position of a point on the Earth's surface.

New!!: Spherical coordinate system and Latitude · See more »

Line element

In geometry, the line element or length element can be informally thought of as a line segment associated with an infinitesimal displacement vector in a metric space.

New!!: Spherical coordinate system and Line element · See more »

Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.

New!!: Spherical coordinate system and Linear algebra · See more »

List of common coordinate transformations

This is a list of some of the most commonly used coordinate transformations.

New!!: Spherical coordinate system and List of common coordinate transformations · See more »

Longitude

Longitude, is a geographic coordinate that specifies the east-west position of a point on the Earth's surface.

New!!: Spherical coordinate system and Longitude · See more »

Loudspeaker

A loudspeaker (or loud-speaker or speaker) is an electroacoustic transducer; which converts an electrical audio signal into a corresponding sound.

New!!: Spherical coordinate system and Loudspeaker · See more »

Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

New!!: Spherical coordinate system and Mathematics · See more »

MathWorld

MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein.

New!!: Spherical coordinate system and MathWorld · See more »

Meridian (geography)

A (geographical) meridian (or line of longitude) is the half of an imaginary great circle on the Earth's surface, terminated by the North Pole and the South Pole, connecting points of equal longitude.

New!!: Spherical coordinate system and Meridian (geography) · See more »

Milky Way

The Milky Way is the galaxy that contains our Solar System.

New!!: Spherical coordinate system and Milky Way · See more »

Multiple integral

The multiple integral is a definite integral of a function of more than one real variable, for example, or.

New!!: Spherical coordinate system and Multiple integral · See more »

North

North is one of the four compass points or cardinal directions.

New!!: Spherical coordinate system and North · See more »

Partial differential equation

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.

New!!: Spherical coordinate system and Partial differential equation · See more »

Phi

Phi (uppercase Φ, lowercase φ or ϕ; ϕεῖ pheî; φι fi) is the 21st letter of the Greek alphabet.

New!!: Spherical coordinate system and Phi · See more »

Philip M. Morse

Philip McCord Morse (August 6, 19035 September 1985), was an American physicist, administrator and pioneer of operations research (OR) in World War II.

New!!: Spherical coordinate system and Philip M. Morse · See more »

Polar coordinate system

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

New!!: Spherical coordinate system and Polar coordinate system · See more »

Position (vector)

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference origin O. Usually denoted x, r, or s, it corresponds to the straight-line from O to P. The term "position vector" is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus.

New!!: Spherical coordinate system and Position (vector) · See more »

Prime meridian

A prime meridian is a meridian (a line of longitude) in a geographic coordinate system at which longitude is defined to be 0°.

New!!: Spherical coordinate system and Prime meridian · See more »

Projection (linear algebra)

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.

New!!: Spherical coordinate system and Projection (linear algebra) · See more »

Radian

The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics.

New!!: Spherical coordinate system and Radian · See more »

Rho

Rho (uppercase Ρ, lowercase ρ or ϱ; ῥῶ) is the 17th letter of the Greek alphabet.

New!!: Spherical coordinate system and Rho · See more »

Right-hand rule

In mathematics and physics, the right-hand rule is a common mnemonic for understanding orientation conventions for the vector cross product in three dimensions.

New!!: Spherical coordinate system and Right-hand rule · See more »

Rotation around a fixed axis

Rotation around a fixed axis or about a fixed axis of revolution or motion with respect to a fixed axis of rotation is a special case of rotational motion.

New!!: Spherical coordinate system and Rotation around a fixed axis · See more »

Rotation matrix

In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space.

New!!: Spherical coordinate system and Rotation matrix · See more »

Sea level

Mean sea level (MSL) (often shortened to sea level) is an average level of the surface of one or more of Earth's oceans from which heights such as elevations may be measured.

New!!: Spherical coordinate system and Sea level · See more »

Separation of variables

In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation.

New!!: Spherical coordinate system and Separation of variables · See more »

Solid angle

In geometry, a solid angle (symbol) is a measure of the amount of the field of view from some particular point that a given object covers.

New!!: Spherical coordinate system and Solid angle · See more »

Sphere

A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").

New!!: Spherical coordinate system and Sphere · See more »

Spherical harmonics

In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere.

New!!: Spherical coordinate system and Spherical harmonics · See more »

Sun

The Sun is the star at the center of the Solar System.

New!!: Spherical coordinate system and Sun · See more »

Theodolite

A theodolite is a precision instrument for measuring angles in the horizontal and vertical planes.

New!!: Spherical coordinate system and Theodolite · See more »

Theta

Theta (uppercase Θ or ϴ, lowercase θ (which resembles digit 0 with horizontal line) or ϑ; θῆτα thē̂ta; Modern: θήτα| thī́ta) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth.

New!!: Spherical coordinate system and Theta · See more »

Unit vector

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.

New!!: Spherical coordinate system and Unit vector · See more »

Vector fields in cylindrical and spherical coordinates

NOTE: This page uses common physics notation for spherical coordinates, in which \theta is the angle between the z axis and the radius vector connecting the origin to the point in question, while \phi is the angle between the projection of the radius vector onto the x-y plane and the x axis.

New!!: Spherical coordinate system and Vector fields in cylindrical and spherical coordinates · See more »

Video game development

Video game development is the process of creating a video game.

New!!: Spherical coordinate system and Video game development · See more »

Volume element

In mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates.

New!!: Spherical coordinate system and Volume element · See more »

World Geodetic System

The World Geodetic System (WGS) is a standard for use in cartography, geodesy, and satellite navigation including GPS.

New!!: Spherical coordinate system and World Geodetic System · See more »

Zenith

The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere.

New!!: Spherical coordinate system and Zenith · See more »

Redirects here:

Angle of elevation, Angular coordinate, Angular coordinate system, Angular coordinates, Elevation angle, Spherical co-ordinates, Spherical coordinate, Spherical coordinates, Spherical cordinates, Spherical polar coordinates, Spherical polars, Spherical system.

References

[1] https://en.wikipedia.org/wiki/Spherical_coordinate_system

OutgoingIncoming
Hey! We are on Facebook now! »