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Topic: Spherical coordinates

Related Topics

Polar coordinate system

Coordinate system

Nabla in cylindrical and spherical coordinates

Vector fields in cylindrical and spherical coordinates

Cartesian coordinate system

Unit vector

Latitude and Longitude

Geographic coordinates

Coordinate rotation

Geographic coordinate system

Geographic coordinate conversion

Yaw, pitch and roll

Spherical geometry

Spherical trigonometry

Longitude

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	Coordinates (mathematics) - Wikipedia, the free encyclopedia
		The coordinates of a point are the components of a tuple of numbers used to represent the location of the point in the plane or space.
		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.
		In terms of the Cartesian coordinate system, one usually picks O to be the origin (0,0) and L to be the positive x-axis (the right half of the x-axis).
	en.wikipedia.org /wiki/Coordinates_(elementary_mathematics) (1186 words)

	PlanetMath: spherical coordinates
		Spherical coordinates are a system of coordinates on the sphere in
		Spherical coordinates are a generalization of polar coordinates, and can be further generalized to the
		This is version 4 of spherical coordinates, born on 2003-07-22, modified 2004-11-17.
	planetmath.org /encyclopedia/SphericalCoordinates.html (104 words)

	Spherical coordinates of icosahedral water clusters
		Use of spherical coordinates is nicely applicable to symmetrical systems with molecules positioned on nested concentric spherical surfaces, such as the icosahedral water cluster.
		Spherical coordinates of the water oxygen atoms in icosahedral water clusters (ES).
		Spherical coordinates of the water oxygen atoms in a super cluster of 13 icosahedral water clusters (ES).
	www.lsbu.ac.uk /water/spher.html (203 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.
	mathforum.org /dr.math/faq/formulas/faq.spherical.html (313 words)

	MATH 2422 #4: 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.
		However, instead of the r coordinate, another polar coordinate system is drawn along the r-ray with the z axis as the polar axis.
		The coordinate surfaces are rho = a (a sphere),
	www-math.cudenver.edu /~rbyrne/online/s00/2422w4.htm (391 words)

	Coordinates (elementary mathematics)
		The circular coordinate system, often referred to 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.
		In the spherical coordinate system, a point P is represented by a tuple of three components
		Spherical coordinates are useful in analyzing systems that are symmetrical about a point; a sphere that has the Cartesian equation
	www.sciencedaily.com /encyclopedia/coordinates__elementary_mathematics_ (795 words)

	Simple Science Wiki: Spherical Coordinate System (Site not responding. Last check: 2007-10-06)
		Spherical coordinates have coordinates typically named (r, θ, φ) where r is a real number and the others are angle measurements.
		Both spherical coordinates and cylindrical coordinates are extensions of the two dimensional polar coordinate system.
		Unlike the Cartesian coordinate system, spherical coordinates include some redundancy in naming points, especially ones on the z-axis.
	www.renaissoft.com /april/cgi-bin/wiki.pl?Spherical_Coordinate_System (182 words)

	Coordinate Systems
		In polar coordinates, a point in the plane is determined by its distance r from the origin and the angle theta (in radians) between the line from the origin to the point and the x-axis (see the figure below).
		Cylindrical coordinates are obtained by replacing the x and y coordinates with the polar coordinates r and theta (and leaving the z coordinate unchanged).
		The coordinates used in spherical coordinates are rho, theta, and phi.
	www.math.oregonstate.edu /home/programs/undergrad/CalculusQuestStudyGuides/vcalc/coord/coord.html (476 words)

	fast marching in spherical coordinates
		As a result, traveltime calculation using equation (4) in spherical coordinates is always exact in homogeneous media.
		Unlike the implementation in Cartesian coordinate, the heap array size in polar coordinates tends to be stable; as we extract a grid point, we usually insert another.
		Even with the polar coordinate system, the majority of the errors occur when the wavefront is at a 45 degree angle to the grid configuration.
	sepwww.stanford.edu /public/docs/sep95/tariq5/paper_html/node4.html (522 words)

	Calculus III (Math 2415) - 3-Dimensional Space - Spherical Coordinates (Site not responding. Last check: 2007-10-06)
		Next, let’s find the Cartesian coordinates of the same point. To do this we’ll start with the cylindrical conversion formulas from the previous section.
		Converting points from Cartesian or cylindrical coordinates into spherical coordinates is usually done with the same conversion formulas. To see how this is done let’s work an example of each.
		So, as we saw in the last part of the previous example it will sometimes be easier to convert equations in spherical coordinates into cylindrical coordinates before converting into Cartesian coordinates. This won’t always be easier, but it can make some of the conversions quicker and easier.
	tutorial.math.lamar.edu /AllBrowsers/2415/SphericalCoords.asp (1073 words)

	Spherical coordinates in integrals (Site not responding. Last check: 2007-10-06)
		When you convert to spherical coordinates Rho, Theta, Phi (with Phi the angle between the radius vector and the z-axis), the volume element dV is not (dRho) * (dTheta) * (dPhi), it is (Rho^2) * (sin(Phi)) * (dRho) * (dTheta) * (dPhi).
		For rectangular coordinates, it is easy -- you form a box with sides dx, dy, and dz.
		Hence, in spheri- cal coordinates dV = (dRho) * (Rho * dPhi) * (Rho * sin(Phi) * dTheta).
	www.newton.dep.anl.gov /newton/askasci/1995/math/MATH133.HTM (325 words)

	FlexPDE User's Forum: Spherical Coordinates
		This requires transformation of the equation, because the "r" coordinate is now the cylindrical radius, not the spherical one.
		FlexPDE does not explicitly treat spherical coordinates, but this case is easily handled as a cylindrical system (with the caveat that "r" is the cylindrical radius coordinate, not the spherical one).
		In cylindrical coordinates, FlexPDE assumes that your 2D mesh layout is a cross-section along the axis of a cylinder, and rotates the figure about the axis.
	www.pdesolutions.com /discus/messages/4/175.html (467 words)

	17.3 The Divergence in Spherical Coordinates
		When you describe vectors in spherical or cylindric coordinates, that is, write vectors as sums of multiples of unit vectors in the directions defined by these coordinates, you encounter a problem in computing derivatives.
		The unit vectors themselves change as you change coordinates, so that the change in your vector consists of terms arising from the changes of the multiples and also those from changes in the unit vectors.
		and this is the form of the divergence in spherical coordinates.
	www-math.mit.edu /18.013A/HTML/chapter17/section03.html (597 words)

	Spherical coordinates
		Spherical coordinates can take a little bit to get used to.
		For these spherical coordinate demos, you can click and drag the blue points along the sliders to change the parameters.
		These three next CVTs may help you understand what each of three spherical coordinates means.
	www.math.umn.edu /~nykamp/m2374/readings/sphcoord (351 words)

	Spherical Coordinates
		In each case two great circles are taken as standards of reference, and the position of the star is determined by means of two quantities called spherical coordinates.
		The vernal equinox (first point of Aries) is the intersection of the equator with the annual path of the sun in March as the declination of the sun changes from South to North.
		If we consider as great circles of reference the horizontal plane at the position of the observer, and his celestial meridian, the coordinates of the star are its altitude and azimuth.
	www.angelfire.com /nt/navtrig/E3.html (511 words)

	Polar Coordinates
		The 2-D polar coordinate system involves the distance from the origin and an azimuth angle.
		The polar coordinates are useful in describing the human body motion since the essence of the human body motion is the joint motions.
		In some cases, one may use the Cartesian coordinates in the sense of the polar coordinates, as shown on
	kwon3d.com /theory/crdsys/polar.html (408 words)

	Spherical Coordinates (Site not responding. Last check: 2007-10-06)
		Spherical coordinates are important to physicists because they make certain problems alot easier (problems like finding the electric potential of a sphere.
		Much easier to do in spherical coordinates than in cartesian).
		In this problem you'll be given, r, theta and phi and will have to convert them over to x, y, and z.
	www.eecis.udel.edu /~breech/contest.inet.spring.00/problems/spherical.html (221 words)

	Spherical Coordinates (Site not responding. Last check: 2007-10-06)
		In the last module we looked at cylindrical coordinates -- a system of coordinates that is very useful when the important things about a three-dimensional point are its distance from the z-axis and its angle from the positive xz-plane.
		The third coordinate -- theta -- is identical to the coordinate theta used in cylindrical coordinates.
		This system of coordinates is very similar to the system -- longitude and latitude -- of coordinates used to describe points on the earth's surface.
	www.math.montana.edu /frankw/ccp/multiworld/multipleIVP/spherical/body.htm (1849 words)

	Triple Integrals in Cylindrical and Spherical Coordinates (Site not responding. Last check: 2007-10-06)
		When we were working with double integrals, we saw that it was often easier to convert to polar coordinates.
		The region, being inside of a cylinder is ripe for cylindrical coordinates.
		Another coordinate system that often comes into use is the spherical coordinate system.
	ltcconline.net /greenl/courses/202/multipleIntegration/cylindricalSphericalIntegration.htm (171 words)

	MA 1024A Laboratory 3: Surfaces
		Parametric plots of surfaces are usually beyond the scope of this course, but we will present an example in Cartesian coordinates at the end of this section.
		Plotting a surface in spherical coordinates is very similar.
		Sometimes a surface cannot easily be represented in Cartesian, polar, or even spherical coordinates.
	www.math.wpi.edu /Course_Materials/MA1024AB00/lab3/node1.html (1412 words)

	Spherical-Coordinates-Product-Overview
		Spherical Coordinates: System of geometrical coordinates used in designating the location of places on the surface of the earth using Spherical Coordinates.
		Spherical Coordinates list includes places where people live and work such as cities, towns, and villages.
		Latitude, which gives the location of a place north or south of the equator, is expressed by angular measurements ranging from 0° at the equator to 90° at the poles.
	www.meridianworlddata.com /HTML3/Spherical-Coordinates-Product-Overview.htm (481 words)

	[No title] (Site not responding. Last check: 2007-10-06)
		The equations of motion are written in spherical coordinates.
		Estimations of spherical coordinates perturbations for geostationary satellite due to neglected geopotential harmonics are obtained.
		Estimations of spherical coordinates perturbations of near circular and near equatorial satellite due to both separate harmonics and neglected harmonics of geopotential are obtained.
	www.astro.amu.edu.pl /html/IAU_Coll/Abstracts/s51.htm (139 words)

	spherical polar coordinates (Site not responding. Last check: 2007-10-06)
		Your calculation is quite likely to involve some function given in terms of the x, y and z coordinates of the point P. In this case you will need to know how to convert the x, y and z into spherical polar terms.
		If this body is spherically symmetric, the working out is much simpler if you replace the little rectangular boxes with the little curved boxes which you get if you let the point P move so that each of its 3 polar coordinates increases separately by an infinitesimally tiny bit.
		Now, suppose you are told some function like density, for example, which is defined in terms of the x,y,z coordinates of each point P of some spherically symmetric body.
	www.netcomuk.co.uk /~jenolive/polar.html (402 words)

	Cylindrical and Spherical Coordinates - Eduseek (Site not responding. Last check: 2007-10-06)
		Cartesian, Cylindrical, and Spherical Coordinates - Shows the relationship between Cartesian, Cylindrical, and Spherical Coordinates with a diagram and equations.
		Introduction to Spherical Coordinates - Basic introduction to Spherical Coordinates, discussing their common uses.
		Spherical Coordinates Overview - An overview of Spherical Coordinates, with equations.
	www.eduseek.com /static/navigate8142.html (215 words)

	[No title] (Site not responding. Last check: 2007-10-06)
		So, for the purpose of this specific article, let us simply assume that a projection is a set of formulas which convert the angular spherical coordinates of latitude and longitude to the linear cartesian coordinates of X and Y.
		Note also, that in the cartesian coordinate system, having a vertical Y axis and a horizontal X axis is also a convention.
		When given a map or set of coordinates to process, be sure to obtain the datum, and the unit of the coordinate system in addition to the zone.
	www.mentorsoftwareinc.com /CC/gistips/TIPS1199.HTM (1824 words)

	Mathematica Code for SeaShell (Site not responding. Last check: 2007-10-06)
		This seashell is brought to you courtesy of spherical coordinates.
		Here are the formulas for transforming spherical coordinates to Cartesian coordinates.
		Using spherical coordinates, we can graph a semicircle of radius 2.
	www.ma.iup.edu /MathDept/Projects/CalcDEMma/SeaShellCode.html (249 words)

	Spherical Coordinates and the GPS (Site not responding. Last check: 2007-10-06)
		The coordinates of each of the two points are given in the form
		In spherical coordinates we measure the angle phi from the north pole.
		In spherical coordinates we measure the angle theta starting at the prime meridian (longitude 0) and moving east.
	www.math.montana.edu /frankw/ccp/cases/Global-Positioning/spherical-coordinates/learn.htm (574 words)

	Appendices: Mathematical Operators
		On a few accompanying pages, we have detailed the specific form that this operator takes in Cartesian, cylindrical, or spherical coordinates.
		While this very general, interactive tool is potentially very powerful, it is strongly recommended that you not try to use it until you have had some experience using the related, but less general, applications that have been taylored for Cartesian, cylindrical, or spherical coordinates.
		The general (curvilinear coordinate) form of the Laplacian operator that is valid in any orthogonal coordinate system is:
	www.phys.lsu.edu /astro/H_Book.current/Appendices/Mathematics/operators.text.shtml (745 words)

	Product Wavefunction in Spherical Coordinates (Site not responding. Last check: 2007-10-06)
		The solution to the SEQ in spherical coordinates is a product wave function of the form:
		Rnl is the ‘radial part’, and Ylm are “spherical harmonics.” The Schrodinger equation in spherical coordinates is complicated.
		An appreciation of the problem can be gained by considering only spherically symmetric states (wavefunctions with no angular dependence).
	online.physics.uiuc.edu /courses/phys114/spring04/Lectures/114_11_sp04/sld025.htm (70 words)

	Calculus III (Math 2415) - Multiple Integrals - Triple Integrals in Spherical Coordinates
		In the previous section we looked at doing integrals in terms of cylindrical coordinates and we now need to take a quick look at doing integrals in terms of spherical coordinates.
		First, we need to recall just how spherical coordinates are defined. The following sketch shows the relationship between the Cartesian and spherical coordinate systems.
		Here is a quick sketch of a spherical wedge for reference purposes.
	tutorial.math.lamar.edu /AllBrowsers/2415/TISphericalCoords.asp (428 words)

	Transformation Matrix for Rectangular to Spherical coordinates - GameDev.Net Discussion Forums (Site not responding. Last check: 2007-10-06)
		Posted - 2/18/2005 3:02:43 PM The term 'polar' usually refers to 2d, an analogous name for polar coordinates might be 'circular coordinates'.
		Matrices represent linear transformations, rectangular to spherical coordinates is none.
		What I mean is if instead of spherical coordinates, you use lattitude and longitude you could map the length(max) of your cartesian set longitude and the width(max) to the lattitude or vice versa.
	www.gamedev.net /community/forums/ViewReply.asp?id=1917569 (480 words)

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