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Topic: Cylindrical coordinates


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  Math Forum: Ask Dr. Math FAQ: Cylindrical Coordinates
Cylindrical coordinates are obtained by using polar coordinates in a plane, and then adding a z-axis perpendicular to the plane passing through the pole.
The most common use of cylindrical coordinates is to give the equation of a surface of revolution.
The Math Forum is a research and educational enterprise of the Drexel School of Education.
mathforum.org /dr.math/faq/formulas/faq.cylindrical.html   (240 words)

  
  Cylindrical Coordinates
In rectangular coordinates, it is the sum of the second derivatives with respect to x, y and z.
Cylindrical coordinates is one system in which this works.
In the present case, we are dealing with a cylindrical wavefront that does not divide into half-period zones as neatly as the spherical wavefront.
www.du.edu /~jcalvert/math/cylcoord.htm   (1662 words)

  
  Cylindrical coordinate system - Wikipedia, the free encyclopedia
The cylindrical coordinate system is a three-dimensional coordinate system which essentially extends circular polar coordinates by adding a third coordinate (usually denoted h) which measures the height of a point above the plane.
Thus, the conversion function f from cylindrical coordinates to Cartesian coordinates is f(r,θ,h) = (rcosθ,rsinθ,h).
Cylindrical coordinates are useful in analyzing surfaces that are symmetrical about an axis, with the z-axis chosen as the axis of symmetry.
en.wikipedia.org /wiki/Cylindrical_coordinates   (226 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.
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),
sosnick.uchicago.edu /spherical_cylindrical_rectangular.html   (366 words)

  
 cylindrical coordinates - Search Results - MSN Encarta
- coordinates specifying point in three dimensions: three coordinates that specify the position of a point in three dimensions by using polar coordinates in one plane and specifying the perpendicular distance of the point from the plane
Coordinate, the elements of an ordered set of numbers that together describe the exact position of something, such as a place on a map, with...
Coordinate System (mathematics), system for identifying elements in a set of points by labeling them with numbers.
encarta.msn.com /cylindrical+coordinates.html   (158 words)

  
 Lab #4   (Site not responding. Last check: )
Cylindrical coordinates are simply polar coordinates,  (r,θ),  with a third dimension  (z) added on.
Cylindrical coordinates are used whenever you have something that is "round" meaning that it has symmetry about the z axis.
If you are an engineer then cylindrical coordinates are used for situations like fluid flow through pipes or arteries, objects machines on lathes, fields about wires and so on.
users.wpi.edu /~goulet/Calc4_04/Lab4.htm   (594 words)

  
 Triple Integrals in Cylindrical and Spherical Coordinates
Cylindrical coordinates are obtained from Cartesian coordinates by replacing the x and y coordinates with polar coordinates r and theta and leaving the z coordinate unchanged.
In rectangular coordinates the volume element dV is given by dV=dxdydz, and corresponds to the volume of an infinitesimal region between x and x+dx, y and y+dy, and z and z+dz.
In cylindrical coordinates, we have dV=rdzdrd(theta), which is the volume of an infinitesimal sector between z and z+dz, r and r+dr, and theta and theta+d(theta).
www.math.oregonstate.edu /home/programs/undergrad/CalculusQuestStudyGuides/vcalc/255cs/255cs.html#spherical   (570 words)

  
 Cylindrical coordinates - DmWiki
Cylindrical coordinates are another way of describing a point in space.
Instead of describing the point as the distance away from the origin in the horizontal (x), vertical (y) and depth (z) directions cylindrical coordinates uses the distance in the radial (r), angular (θ) and depth (z) directions.
It is possible to convert from Cartesian coordinates to cylindrical coordinates.
www.devmaster.net /wiki/Cylindrical_coordinates   (253 words)

  
 Autodesk - AutoCAD - Introduction to 3D Coordinates   (Site not responding. Last check: )
Cylindrical coordinates are unique to 3D and are somewhat similar to polar coordinates in 2D.
The result is a new coordinate (in this case 7,3—the x coordinate of the first endpoint and the y coordinate of the second endpoint).
The result is a new coordinate (in this case 7,4,6—the xy coordinate of the first endpoint and the z coordinate of the second endpoint).
usa.autodesk.com /adsk/servlet/item?siteID=123112&id=3028436&linkID=2475176   (1597 words)

  
 Cylindrical Coordinate Demonstration   (Site not responding. Last check: )
Cylindrical coordinates are useful for describing points with cylindrical symmetry.
The three cylindrical coordinates are radius, azimuthal angle phi, and z.
The z coordinate is exactly the same as the cartesian z coordinate.
www.pha.jhu.edu /~javalab/cylindrical/cylindrical.html   (221 words)

  
 PlanetMath: Laplace equation in cylindrical coordinates
Solutions to the Laplace equation in cylindrical coordinates have wide applicability from fluid mechanics to electrostatics.
Finally, the use of Bessel functions in the solution reminds us why they are synonymous with the cylindrical domain.
This is version 6 of Laplace equation in cylindrical coordinates, born on 2006-11-14, modified 2006-11-14.
planetmath.org /encyclopedia/LaplaceEquationInCylindricalCoordinates.html   (813 words)

  
 Cylindrical Coordinates
The first coordinate describes the distance from the z-axis to the point and the second coordinate describes the angle from the positive xz-plane to the point.
It is important to compare the units that are used in Cartesian coordinates with the units that are used in cylindrical coordinates.
In cylindrical coordinates, (r, theta, z), two of the coordinates -- r and z -- measure length and, thus, are in units of length but the coordinate theta measures angles and is in "units" of radians.
www.math.montana.edu /frankw/ccp/multiworld/multipleIVP/cylindrical/body.htm   (1127 words)

  
 Spherical Polar Coordinates   (Site not responding. Last check: )
With the axis of the circular cylinder taken as the z-axis, the perpendicular distance from the cylinder axis is designated by r and the azimuthal angle taken to be
Physical systems which have spherical symmetry are often most conveniently treated by using spherical polar coordinates.
Physical systems which have cylindrical symmetry are often most conveniently treated by using cylindrical polar coordinates.
hyperphysics.phy-astr.gsu.edu /hbase/sphc.html   (61 words)

  
 Riemann.html
Therefore the xy plane angle Phi is unaltered by this mapping.
But the coordinates r and vertical distance are changed.
A point of cylindrical radius k maps into a point of radius 1/(k+1/k).
clowder.net /hop/Riemann/Riemann.html   (413 words)

  
 Map Projection Overview
Cylindrical Equal-Area projections have straight meridians and parallels, the meridians are equally spaced, the parallels unequally spaced.
Gall's stereographic cylindrical projection results from projecting the earth's surface from the equator onto a secant cylinder intersected by the globe at 45 degrees north and 45 degrees south.
The Peters projection is a cylindrical equal-area projection that de-emphasizes area exaggerations in high latitudes by shifting the standard parallels to 45 or 47 degrees.
www.colorado.edu /geography/gcraft/notes/mapproj/mapproj.html   (1829 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)

  
 11.7
Cylindrical coordinates is nothing more than adding a z axis above the xy plane when xy is listed in polar coordinates r
) is the points projection onto the xy plane given in polar coordinates, and z is the distance from the xy plane to the point.
Cylindrical coordinates, like polar coordinates, give us a way to simplify the equations of some surfaces.
www.ac.cc.md.us /~donr/CalcIII/unit1/lesson7/u1l7.html   (361 words)

  
 Math Forum: Ask Dr. Math FAQ: Cylindrical Coordinates
Cylindrical coordinates are obtained by using polar coordinates in a plane, and then adding a z-axis perpendicular to the plane passing through the pole.
The most common use of cylindrical coordinates is to give the equation of a surface of revolution.
The Math Forum is a research and educational enterprise of the Drexel School of Education.
www.mathforum.org /dr.math/faq/formulas/faq.cylindrical.html   (240 words)

  
 Understanding Galactic Coordinates   (Site not responding. Last check: )
The galactic coordinate system has latitude and longitude lines, similar to what you are familiar with on Earth.
In the galactic coordinate system the zero degree latitude line is the plane of our galaxy, and the zero degree longitude line is in the direction of the center of our galaxy, towards the constellation Sagittarius.The activity below is designed to help you visualize the galactic coordinate grid.
Printout of the coordinate grid on paper or clear transparency.
cse.ssl.berkeley.edu /chips_epo/coordinates.html   (522 words)

  
 14.7
The x and y coordinates of the center of mass are both 0 from the symmetry of the region.
Keep in mind some regions are very simply defined in spherical coordinates, even though the integration formula may look a bit intimidating.
Also the x and y coordinates are obviously both 0, since the figure is centered on the z axis and symmetrical.
www.ac.cc.md.us /~donr/CalcIII/unit4/lesson7/u4l7.html   (465 words)

  
 FlexPDE User's Forum: DTANGENTIAL BC in cylindrical coordinates
However, for cylindrical coordinates (r,z), and vector potential A (having azimuthal component only), the axial value of the curl is given by (1/r)*Dr(r*A), so that if A is specified as constant (= c), there is a non-zero axial component of (CURL(A))z (= c/r).
In (r,z) coordinates, the azimuthal component of the potential, A = c/r, on the boundary has zero tangential derivative, whereas in Cartesian geometry, A = c on the boundary is the correct value that gives DTANGENTIAL(A) = 0.
To reiterate, I suspect that the implementation of DTANGENTIAL is incorrect for cylindrical 2-D coordinates.
www.pdesolutions.com /cgi-bin/discus/show.cgi?tpc=4&post=821   (837 words)

  
 Isosurface Tutorial: variable Substitution
By transforming from cartesian to cylindrical polar coordinates, it's possible to bend any isosurface into a circle around the origin.
The cylindical polar coordinates are made available through the f_th() and f_r() functions, so you don't have to work them out for yourself.
The spherical polar coordinates are made available through the f_th(), f_r() and f_ph() functions, so you don't have to work them out for yourself.
www.econym.demon.co.uk /isotut/substitute.htm   (1386 words)

  
 9.2 Cylindrical Coordinates in Space
To define cylindrical coordinates, we take an axis (usually called the z-axis) and a perpendicular plane, on which we choose a ray (the initial ray) originating at the intersection of the plane and the axis (the origin).
) of the projection of P on the plane, and the coordinate z of the projection of P on the axis (Figure 1).
,z) of cylindrical coordinates for P are (10,30°,5) and (10,390°,5).
www.geom.uiuc.edu /docs/reference/CRC-formulas/node40.html   (110 words)

  
 fluid dynamics - dissipation using cylindrical coordinates
I have this flow field in cylindrical coordinates of wich I would like to calculate the dissipation as a function of these coordinates.
What does invariance under general coordinates tranformation mean for the expression you wrote down.
Surely the components of e change under a coordinate transormation as the Christoffel symbols change.
www.physicsforums.com /showthread.php?t=72755   (1259 words)

  
 Calculus II (Math 2414) - 3-Dimensional Space - Cylindrical Coordinates   (Site not responding. Last check: )
 coordinate system is called the Cartesian coordinate system.  In the last two sections of this chapter we’ll be looking at some alternate coordinates systems for three dimensional space.
The conversions are the same conversions that we used back in when we were looking at polar coordinates.  So, if we have a point in cylindrical coordinates the Cartesian coordinates can be found by using the following conversions.
Likewise, if we have a point in Cartesian coordinates the cylindrical coordinates can be found by using the following conversions.
tutorial.math.lamar.edu /AllBrowsers/2414/CylindricalCoords.asp   (337 words)

  
 FlexPDE User's Forum: 3D Cylindrical Coordinates
If P is not a variable, then you have to apply a boundary condition to something that is a variable but reflects the same thing.
Unwrap the cylinder and treat (r,z) as the baseplane coordinates and theta as the extrusion direction.
Apply periodic boundary conditions at the top and bottom, and write the equations explicitly in the correct form for the geometry.
www.pdesolutions.com /cgi-bin/discus/show.cgi?tpc=4&post=1170   (216 words)

  
 Best free cylindrical downloads. transforms cartesian, spherical and cylindrical coordinates. Utility: HTML web page, ...
Cylindrical software: Design of 15 springs types, The SP_SC converter is intended for compilin, 360 Spherical Panorama Video Viewer and more.
The calculation is intended for the purposes of geometric and strength designs of helical compression cylindrical springs made of wires and rods of circular sections, cold formed, loaded with static or fatigue loading.
The calculation is intended for the purposes of geometric and strength designs of helical tension cylindrical springs made of wires and rods of circular sections, cold formed, loaded with static loading.
www.freedownloadmanager.org /downloads/cylindrical_software   (611 words)

  
 Mathlets: Cylindrical Coordinates (3-D Graphing)
Graphs one function of the form z=f(r,θ) using cylindrical coordinates in three dimensions.
The text input fields for functions can accept a wide variety of expressions to represent functions, and the buttons under the graph allow various manipulations of the graph coordinates.
The "wireframe" represenation for surfaces, in which the surface is transparent, only draws one surface at a time.
cs.jsu.edu /mcis/faculty/leathrum/Mathlets/cylindrical.html   (265 words)

  
 Project Links | Gradient
The gradient in rectangular coordinates is given by
To express the gradient in cylindrical coordinates, consider as a function of and note that and.
Finally, since the gradient in cylindrical coordinates is expressed as
www.ibiblio.org /links/devmodules/gradient/html/cylindrical_theory.html   (90 words)

  
 Triple Integrals in Cylindrical and Spherical Coordinates
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.
www.ltcconline.net /greenl/courses/202/multipleIntegration/cylindricalSphericalIntegration.htm   (171 words)

  
 Boundary conditions in cylindrical coordinates. - Numerical Recipes Forum
The question is for all who have ever used five-point Laplas approximation in cylindrical coordinates.
As the coordinate lines phi=constant (phi is the angular coordinate) converge toward r=0, the derivative of the dependent variable u (say) with respect to phi must become zero, so that u(r=0,phi)=constant.
As a rule, I usually use cell-centered discretizations when the coordinates contain a singularity, which avoids a lot of the problems associated with them.
www.nr.com /forum/showthread.php?t=504   (554 words)

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