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Topic: Spherical coordinate system

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	Encyclopedia :: encyclopedia : Coordinates (elementary mathematics) (Site not responding. Last check: 2007-10-19)
		The polar coordinate systems are coordinate systems in which a point is identified by a distance from some fixed feature in space and one or more subtended angles.
		The cylindrical coordinate system is a three-dimensional polar coordinate system.
		The spherical coordinate system is a three-dimensional polar coordinate system.
	www.hallencyclopedia.com /Coordinates_(elementary_mathematics) (1339 words)

	Antenna Apherical Coordinate Systems
		coordinates with the Z-axis as the polar axis.
		With this rotator, the origin of the AUT coordinate system is not centered on the antenna.
		In a sense the "natural" coordinate system is the one that corresponds to the vector components since the field vectors are along the lines of the corresponding coordinates.
	www.nearfield.com /amta/Amta99_0_an-gh.htm (2537 words)

	CYLINDRICAL AND SPHERICAL COORDINATES
		The coordinate surfaces for the rectangular coordinate system are the planes perpendicular to the coordinate axes, x = a, y = b, and z = c.
		The coordinate surfaces for the cylindrical coordinate system is: r = a (a cylinder),
		However, instead of the r coordinate, another polar coordinate system is drawn along the r-ray with the z axis as the polar axis.
	sosnick.uchicago.edu /spherical_cylindrical_rectangular.html (366 words)

	Spherical_coordinate_system Information, explanation, recent texts, monographs, and related patents.
		Polar coordinates The polar coordinate systems are coordinate systems in which a point is identified by a distance from some fixed feature in space and one or more subtended angles.
		Circular coordinates The circular coordinate system, often called simply as the polar coordinate system, is a two-dimensional polar coordinate system, defined by an origin, O, and a semi-infinite line L leading from this point.
		Spherical coordinates The spherical coordinate system is a three-dimensional polar coordinate.
	www.prime-radiant.com /primary/science-plus-computers/Spherical_coordinate_system.html (1358 words)

	Cartographiometry Glossary of Terms
		Spherical geometry is the study of figures on the surface of a sphere in much the same way that Euclidean geometry is the study of figures in a plane.
		The polar coordinate system is a coordinate system in the plane based on the selection of a point, designated as the origin of the system, and a reference direction (really a half-line emanating from the selected origin).
		The spherical coordinate system is a coordinate system on a given sphere based on the selection of a pair of antipodal (opposite) points, designated as the poles of the system.
	www06.homepage.villanova.edu /timothy.feeman/cartography/textsupp/keywords.htm (3332 words)

	Appendix A
		The rectangular coordinate system should be right-handed to be consistent with conventions in the physical sciences and to permit straightforward application of the standard equations used in vector analysis and electromagnetism.
		In the illustrative spherical coordinate system, the vector magnitude is represented by the symbol M (being the same as the radius vector r in the spherical polar coordinate system).
		The consistent coordinate system differs from that recommended by the American Heart Association (1967), and the conversion of the respective coordinate axes and angles is as shown in Table A.1.
	butler.cc.tut.fi /~malmivuo/bem/bembook/aa/aa.htm (1473 words)

	Spherical coordinate system : Spherical coordinates
		Spherical coordinates have coordinates typically named $(r, \theta, \phi)$ where the radius $r$ range from 0 to $\infin$ , the colatitude $\theta$ range from 0 to π and the azimuth $\phi$ range from 0 to 2π.
		There are conversions between Cartesian and spherical coordinates based on trigonometric functions.
		Both spherical coordinates and cylindrical coordinates are extensions of the two dimensional polar coordinate system.
	www.fastload.org /sp/Spherical_coordinates.html (277 words)

	Chapter 18 Reference Frames and Coordinate Systems
		A system of coordinates must be established to uniquely describe a position in space or to describe the magnitude and direction of target velocity with respect to a specified reference frame.
		The rectangular or Cartesian coordinate system employs the target's range in the true north/south direction as the Y-axis distance, the target's range in the east/west direction as the X-axis distance, and the vertical height as the Z-axis distance.
		Coordinate conversion is the process of changing from one system of coordinates that describe a point within a reference frame to another system of coordinates describing the same point in the same reference frame.
	www.fas.org /man/dod-101/navy/docs/fun/part18.htm (3404 words)

	Wyoming GIS Coordination Structure (Site not responding. Last check: 2007-10-19)
		coordinate systems - a particular kind of reference frame or system, such as plane rectangular coordinates or spherical coordinates, that use linear or angular quantities to designate the position of points used to represent locations on the earth’s surface relative to other locations or fixed references.
		In planimetric mapping (two dimensional coordinate system) locations are represented by x, 6, coordinate pairs while in topographic mapping (three dimensional coordinate system) locations are represented by x, y, and z values.
		Overlays are registered to the base data by a common coordinate system.
	wgiac2.state.wy.us /html/whatisgis.asp (3223 words)

	Setting Your GPS Datum and Coordinate System
		The datum setting in a GPS receiver is a reference which describes the origin and orientation of coordinate systems we use on maps to identify points on the earth's surface.
		Since UTM coordinates are given as pairs referenced to the southwest corner of a rectangle they are read from west to east for the Easting and south to north for the Northing.
		Coordinate pairs can be abbreviated on maps by dropping the last three digits, writing them to a resolution of 1000 meters.
	www.alpharubicon.com /prepinfo/mapdatumwmerrin.htm (1632 words)

	lesson 6 (Site not responding. Last check: 2007-10-19)
		In this case, you must use the 2-D spherical coordinate system (theta and phi); you cannot use rectangular coodinates because you CANNOT tile the surface of a sphere by squares.
		For rectangular coordinates: The unit vectors are i, j, k amd the coressponding scale factors are 1, 1, 1.
		For spherical coordiantes: The unit vectors are r hat, theta hat, and phi hat and teh corresponding scale factors are 1, r, and r sin (theta).
	www2.hawaii.edu /~plam/ph400/lesson6.html (400 words)

	CONSTRUCT COORDSYS SPHERICAL
		Local spherical coordinate systems may be selected for use in the definition of point coordinates (in terms of the local spherical coordinates
		Each time that a new axis system is created an axis set is drawn at the local origin to indicate the location and orientation of the coordinate system.
		When the resulting spherical system is used with RESULTS LOCAL TRANSFORM the radial (or local x) direction is normal to the surface of the sphere, the hoop (or local y) direction is in a plane normal to the axis and the local z direction is perpendicular to these two.
	www.princeton.edu /~dynaflow/femgv/manuals/userman/node68.htm (354 words)

	Math Forum: Ask Dr. Math FAQ: Spherical Coordinates
		Spherical coordinates are obtained by using polar coordinates in a plane, adding a vertical axis perpendicular to the plane passing through the pole, and assigning a positive direction to it.
		The first coordinate of any point P is the distance rho of P from the pole O. The second coordinate of P is the angle theta from the polar axis to the projection of OP into the plane.
		The third coordinate of P is the angle phi between that positive part of the vertical axis and the line segment OP.
	www.mathforum.org /dr.math/faq/formulas/faq.spherical.html (299 words)

	Earth Coordinate System
		The horizontal coordinate system (commonly referred to as the alt-az system) is the simplest coordinate system as it is based on the observer's horizon.
		A more convenient coordinate system for cataloging purposes is one based on the celestial equator and the celestial poles and defined in a similar manner to latitude and longitude on the surface of the Earth.
		In this system, known as the equatorial coordinate system, the analog of latitude is the declination,
	zebu.uoregon.edu /~js/ast121/lectures/lec03.html (2904 words)

	Spherical Coordinate System Lab
		This coordinate system is based upon the physical fact that we live on the earth and gravity pulls us to the earth establishing and up and a down locally.
		This coordinate system is based upon the physical fact that the earth revolves about the sun in a year.
		This coordinate system is based upon the physical fact that we live in a flattened disk of stars that the solar system revolves about in approximately 250 million years.
	www.mc.cc.md.us /Departments/planet/planet/Coordinate_Systems_Lab.htm (1626 words)

	Coordinate Systems
		The numbers assigned to a position, or point, are called the coordinates of that point (in the coordinate system under consideration).
		In physical laboratories, and sometimes for everyday purpose, it is convenient to use cartesian coordinates, i.e., just length, width and height measured from a reference point (the origin of the system) in three mutually othogonal (or perpendicular) directions, i.e., three straight lines called axes of the coordinate system, which have mutually right angles between them.
		Each coordinate system is now uniquely determined by its origin, either its polar axis or the equatorial plane (the other is always perpendicular and thus given by the one), and the reference direction.
	www.seds.org /~spider/spider/ScholarX/coord_bas.html (630 words)

	Project 1 \| Plotting Coordinates and Projections
		Like the spherical coordinate system, lines of latitude are parallel while lines of longitude all intersect at the poles.
		Horizontal datum relate a coordinate system to the surface of the earth.
		The State Plane coordinate system also allows for easy calculations of distance within zones, and has smaller zones than UTM so the error is smaller.
	www.personal.psu.edu /bim105/project1.html (1136 words)

	* Spherical Coordinate System - (GIS): Definition
		Spherical Coordinate System: A coordinate system measured on the surface of a sphere, usually expressed as angular distances.
		In a spherical coordinate system, the vertical line that runs parallel to the earth's rotation, passing through 90 degrees north latitude, and perpendicular to the equatorial plane, where it crosses the x- and y- axes at the origin (0,0,0).
		Latitude- The north/south component of the spherical coordinate system most widely used to record geodetic locations.
	en.mimi.hu /gis/spherical_coordinate_system.html (89 words)

	[No title]
		This option uses the input key pair of column coordinate and returns the rows in the searched table that are within the specified range (distance) of the input point.
		The units specification for a one dimensional coordinate system only determines where axis wraps over to zero, no units conversion is done between the column and range values.
		The units for a one dimensional spherical coordinate system should be explicitly set.
	cfa-www.harvard.edu /~john/starbase/search.html (1073 words)

	T1ReviewSection
		A map coordinate system is an X,Y system that can be used to reference the location of any point on the earth's surface.
		Therefore, flat or planar coordinate systems such as Universal Transverse Mercator (UTM) and the State Plane systems are preferred.
		The system used to portray a part of the round Earth on a flat surface is called a map projection.
	plantsci.sdstate.edu /precisionfarm/AdoptAFarm/Tutorials/T1ReviewSection.htm (1032 words)

	There Wiki: CoordinateSystems
		The main user-visible co-ordinate system in the MetaVerse is a 3-dimensional Cartesian system of X, Y and Z co-ordinates with its origin at the exact centre of PlanetThereia.
		PlanetThereia has a radius of six million metres, in the sense that the reference point for terrain at a given point on the planet is exactly six million metres from X=Y=Z=0; again, this puts it roughly at the same size as planet Earth.
		This means that the origin of the global spherical coordinate system is the same as the origin of the global Cartesian coordinate system.
	www.iay.org.uk /there/wiki/wiki.pl?CoordinateSystems (542 words)

	Special cases of the orthogonal coordinate systems
		The most frequently used coordinate systems are cartesian, circular cylindricaland spherical systems.
		The position of a point A in the cartesian coordinate system is given by the intersection of the three plane coordinate surfaces, see Fig.
		In this system the coordinates and basic unit vectors are denoted as
	www.eaeeie.org /theiere/curvilinear/SpecCasesortCoordSys.htm (280 words)

	Spherical source
		By symmetry, we expect the light vector due to a spherical source to be radially symmetric, ie, equivalent to a point source located at the sphere's center.
		By choosing this coordinate system, we need not deal with spherical harmonics, but with the simpler Legendre polynomials.
		As shown in appendix A.3, the second bracketed term in Equation 22 is a telescoping sum that collapses to 1.
	www.cs.princeton.edu /~ah/publications/multipole/html/node11.html (260 words)

	3-D coordinate systems
		Each coordinate axis is given a direction in which its values grow and a scale.
		A point in spherical coordinate system is given by the end of the vector drawn from the point of origin and is specified by 3 coordinates: R - the length of the vector (the radius of the imaginary sphere), l - the latitude of the point and p - the longitude of the point.
		The longitude is the angle between the projection of the vector on the equatorial plane (xOy plane) and the plane of the zero meridian (xOz plane).
	www.stavr.com /math/d3graph.htm (595 words)

	SPEC: spherical-coordinate-system (Site not responding. Last check: 2007-10-19)
		A {spherical-coordinate-system} is a coordinate system in 3-space specified by distance r, and angles phi and theta.
		Returns a 3 element vector in which the first component gives the units-per-meter of the r coordinate, the second component gives the units-per-radian of the phi coordinate, and the third component gives the units-per-radian of the theta coordinate.
		Each number gives the absolute scale of the corresponding coordinate axis in units per meter or radian, as appropriate.
	www.ai.mit.edu /extra/tools/iue-docs/docs/AAI/IUE/spec/coordsys/spherical-coordinate-system.html (74 words)

	Interpreting Antenna Performance Parameters for EMC Applications - Part 2
		Traditional spherical coordinates consist of a radial distance, an elevation angle, and an azimuthal angle as shown in Figure 1.
		These spherical coordinates are analogous to the more familiar coordinates on a globe: azimuthal angle is equivalent to longitude; elevation angle is the complement of latitude (it is sometimes referred to as co-latitude).
		In communications systems, where antennas are generally always quite widely separated, it is sufficient to be concerned only with the far field of an antenna.
	www.djmelectronics.com /articles/emc-antenna-parameters-p2.html (3904 words)

	intro3e
		For a spherically symmetric scatterer and a proper choice of the spherical coordinate system one can separate the variables both in the equation and the boundary conditions and obtain the solution in the explicit form (so called Mie theory - see, e.g., [1]).
		Here in contrast with the case of spheres, the proper choice of the directions of the axes of the Cartesian coordinate systems (there are usually two required systems - the laboratory one and that connected with the scatterer) plays in particular important role.
		The absence of symmetry in the spatial distribution of the scattered radiation leads to the fact that the total recoil of scattered photons is not directed along the direction of propagation of the incident radiation.
	www.astro.spbu.ru /DOP/1-DEFS/INTROD (1060 words)

	Background: Dipole approximations of the geomagnetic field
		In this frame of reference, we define a system of spherical coordinates (r, theta, phi) whose polar axis coincides with the Z-axis.
		The sum of terms with n = 1 in the expansion reduces to one term in the spherical coordinate system with centre at the Earth's centre and polar axis coinciding with the geomagnetic axis.
		Bartels (1936) is to minimize the terms of second order in the potential used in the spherical harmonic representation of the field.
	www.spenvis.oma.be /spenvis/help/background/magfield/cd.html (1953 words)

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