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Topic: Cylindrical coordinate system

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Spherical coordinate system

Coordinate system

Cartesian coordinate system

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	Coordinate system - Wikipedia, the free encyclopedia
		Curvilinear coordinates are a generalization of coordinate systems generally; the system is based on the intersection of curves.
		Circular coordinate system (commonly referred to as the polar coordinate system) represents a point in space by an angle and a distance from the origin.
		Cylindrical coordinate system represents a point in space by an angle, a distance from the origin and a height.
	en.wikipedia.org /wiki/Coordinate_system (1155 words)

	Cylindrical coordinate system - Wikipedia, the free encyclopedia
		The cylindrical coordinate system is a three-dimensional 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.
		Cylindrical coordinates are useful in analyzing surfaces that are symmetrical about an axis, with the z-axis chosen as the axis of symmetry.
		In many problems involving cylindrical polar coordinates, it is useful to know the line and volume elements; these are used in integration to solve problems involving paths and volumes.
	en.wikipedia.org /wiki/Cylindrical_coordinate_system (277 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)

	Boundary fitted coordinates
		The basic idea of a boundary-conforming curvilinear coordinate system is to have some coordinate line (in 2D, surface in 3D) coincident with each boundary segment, analogous to the way in which lines of constant radial coordinate coincide with circles in the cylindrical coordinate system.
		The other curvilinear coordinate, analogous to the angular coordinate in the cylindrical system, will vary along the boundary segment and clearly must do so monotonically, else the same pair of values of the curvilinear coordinates will occur at two different physical points.
		There must, or course, be a unique correspondence between the Cartesian (or other basis system) and the curvilinear coordinates, i.e., the mapping of the physical region onto the transformed region must be one-to-one, so that every point in the physical field corresponds to one, and only one, point in the transformed field, and vice versa.
	www.cse.ucsc.edu /~shreyas/btp/node14.html (442 words)

	Surface loads: Define distributed loads on surface elements, calculate statically equivalent forces
		Edges of the load area and of the elements must be parallel to the axis of the local coordinate system.
		Edges of the loaded area and of the elements must be parallel to the axis of the cylindrical coordinate system.
		The components of the resultant and its position relative to the local coordinate system are displayed in the protocol window.
	www.g-boege.de /english/makrosae/Manual/Surface_loads.htm (1322 words)

	ipedia.com: Coordinate system Article (Site not responding. Last check: 2007-10-09)
		See Cartesian coordinate system or Coordinates for a more elementary introduction to this topic In mathematics as applied to geometry, physics or engineering, a coordinate system is a system for assig...
		In mathematics as applied to geometry, physics or engineering, a coordinate system is a system for assigning a tuple of scalars to each point in an n-dimensional space.
		a mapping of points to other points which distorts a rectangle to a parallelogram changes the coordinates the same as keeping the points in place but changing the basis vectors from being two sides of that parallellogram to perpendicular ones, two sides of that rectangle.
	www.ipedia.com /coordinate_system.html (629 words)

	Coordinates elementary mathematics - Wikipedia, the free encyclopedia
		Look for Coordinates elementary mathematics in Wiktionary, our sister dictionary project.
		Look for Coordinates elementary mathematics in the Commons, our repository for free images, music, sound, and video.
		Check for Coordinates elementary mathematics in the deletion log, or visit its deletion vote page if it exists.
	www.sciencedaily.com /encyclopedia/coordinates__elementary_mathematics_ (166 words)

	VIAS Encyclopedia: Cylindrical Coordinate System (Site not responding. Last check: 2007-10-09)
		The cylindrical coordinate system specifies the position of a point P by the combination of its distance to the z-axis (radius
		To specify a particular point in a cylindrical coordinate system, you indicate the coordinate values in the form [
		coordinate is called azimuthal coordinate, and the z coordinate is also called the applicate.
	www.vias.org /encyclopedia/math_coord_cylinder_3d.htm (122 words)

	Nat' Academies Press, Twenty-Fourth Symposium on Naval Hydrodynamics (2003) (Site not responding. Last check: 2007-10-09)
		Since the stream surfaces are assumed aligned with the cylindrical surfaces, the thickness and the camber of a section are defined on the cylindrical surface with the same radius.
		A possible reason for the root cavitation is that the propeller blade geometry is designed on the cylindrical coordinate system, and the manufacturer extrapolated the blade sections near the root to fit the conical body.
		Figure 2 shows that the calculated circulation distributions are different when the blade sections defined on a cylindrical coordinate system and on a conical coordinate system with the same blade outline, and the difference is not negligible.
	www.nap.edu /openbook/NI000511/html/839.html (6922 words)

	NetCDF Coordinate Conventions: Re: Coordinate Systems Proposals
		The base coordinate system, on the other hand, is the coordinate system in which we normally think of the variable.
		The manifold coordinate system for this is one-dimensional: it is the position along the wire from one end.
		In one sense, "lat" is one of the manifold coordinates (and could have very little to do with latitude); in the other sense, "lat" is a variable that associates a base coordinate (latitude) with every position in the manifold domain.
	www.unidata.ucar.edu /software/netcdf/coords/0074.html (897 words)

	ANSYS Tutorial - Curved Beam Step #4 (Site not responding. Last check: 2007-10-09)
		Four of the keypoints are the vertices A,B,C and D shown in the figure of the geometry.
		The reference number that ANSYS uses for the cylindrical coordinate system is 1 (the Cartesian system is 0).
		When the active coordinate system is set to cylindrical, X, Y, and Z in the menus refer to the cylindrical coordinates r, θ (in degrees) and z, respectively.
	instruct1.cit.cornell.edu /courses/ansys/beam/step04.htm (498 words)

	How to Define a Local Coordinate System
		Enter three sets of coordinates in the "Point A", "Point B" and "Point C" fields to define the local coordinate system per the diagram shown on the screen.
		The active local cylindrical coordinate system is shown in the "Coordinate System" field.
		Local coordinate systems can either be reused in the Superview IV Results environment or defined there to display results in an arbitrary orientation relative to them (see How to Display Results in a Local Coordinate System).
	www.algor.com /service_support/hints_tips/lcs_fea_editor.asp (604 words)

	3D Myocardial Strain Reconstruction From Tagged MRI Using a Cylindrical B-spline Model (Site not responding. Last check: 2007-10-09)
		One problem with Cartesian coordinate B-spline models is that the B-spline model is defined on a rectangular domain and the LV is circular (in the short axis - in the long-axis, it is roughly elliptical).
		The B-spline model is based on a cylindrical coordinate system that more closely fits the morphology of the myocardium than previously proposed Cartesian B-spline models and does not require explicit regularization.
		Simulation results demonstrate that the reconstructed strains are robust to the center of the cylindrical coordinate system.
	www.eng.auburn.edu /users/dengxia/cylBspline.htm (360 words)

	TUTORIAL NUMBER 9
		This means that coordinates are in R, theta and Z instead of X, Y and Z. All coordinates remained labeled x, y and z if, for example, you list the keypoints.
		For a shell element in cylindrical coordinates, r is to the center of the shell.
		Turn on the boundary conditions symbol and the nodal coordinate system symbol and plot the nodes.
	www.und.nodak.edu /instruct/gbibel/T9_Shell_Pipe.htm (803 words)

	CSYS (Site not responding. Last check: 2007-10-09)
		Cylindrical with Y as the axis of rotation
		The active coordinate system for files created via the CDWRITE command is Cartesian (CSYS,0).
		CSYS,5 is a cylindrical coordinate system with Y as the axis.
	www1.ansys.com /customer/content/documentation/80/ansys/Hlp_C_CSYS.html (184 words)

	How to Display Results in a Local Coordinate System
		When displaying a stress tensor relative to a Cartesian coordinate system, the actual hoop stress only occurs in those areas where the stress tensor vector is aligned with the direction of the hoop stress (Figure 1).
		As an alternative, a cylindrical coordinate system can be used so that the actual hoop stress is shown around the full circumference of the model.
		Local coordinate systems can also be defined in the FEA Editor environment to aid in the creation of loads and constraints (see How to Define a Local Coordinate System).
	www.algor.com /service_support/hints_tips/results_lcs.asp (406 words)

	[No title]
		There apparently is no system, hyperbolic or elliptic, that will give complete orthogonality in 3-D. This hyperbolic grid generation system is faster than the elliptic generation systems by one or two orders of magnitude, the computational time required being equivalent to about that for one iteration in a solution of the elliptic system.
		The hyperbolic generation system is not as general as the elliptic systems, however, since the entire boundary of the region cannot be specified.
		The parabolic generation system is also faster than the elliptic generation systems to the same degree as is the hyperbolic system, since again only a succession of tridiagonal solutions is required.
	www.erc.msstate.edu /publications/gridbook/chap07/text.html (1075 words)

	METBD 350: Planning for Project 1 (Site not responding. Last check: 2007-10-09)
		A Cylindrical Coordinate System is needed for pin support B.C. Rotated node coord.
		By default, nodal coordinate systems are parallel to the Global Cartesian.
		Create/Activate a cylindrical coordinate system at the center of the pin
	www.personal.psu.edu /users/d/h/dhj1/classes/lec5_350.html (254 words)

	Thesis Abstract (Site not responding. Last check: 2007-10-09)
		As metallurgical reactor vessels involves both rectangular and cylindrical geometries, 3 D model for Cartesian coordinate system as well as cylindrical coordinate system are required to predict fluid flow in different metallurgical systems theoretically.
		This model was then synthesized with similar model developed by C. Vanu [301 for Cartesian coordinate system and a generalized computer procedure was developed to predict fluid flow in various metal processing operations.
		This model was then synthesized with the model in the Cartesian coordinate system [30] to develop a generalized mathematical framework for the analysis of flow in metallurgical reactors.
	www.iitk.ac.in /mme/mtTheses/2001/9910615.html (276 words)

	Calculus II (Math 2414) - 3-Dimensional Space - Cylindrical Coordinates
		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)

	Frequently Asked Questions (Site not responding. Last check: 2007-10-09)
		I have trouble applying a displacement constraint in the cylindrical coordinate system.
		Constraints are applied to the nodes, which are in the nodal coordinate system.
		If your active coordinate system is cylindrical, NROTATE will rotate them so that y will be the tangential direction for each node.
	instruct1.cit.cornell.edu /courses/ansys/faq.htm (634 words)

	Coordinate Systems (Site not responding. Last check: 2007-10-09)
		The most common coordinate system for representing positions in space is one based on three perpendicular spatial axes generally designated x, y, and z.
		Any point P may be represented by three signed numbers, usually written (x, y, z) where the coordinate is the perpendicular distance from the plane formed by the other two axes.
		Although the entire coordinate system can be rotated, the relationship between the axes is fixed in what is called a right-handed coordinate system.
	hyperphysics.phy-astr.gsu.edu /hbase/coord.html (117 words)

	Coordinate Systems (Site not responding. Last check: 2007-10-09)
		They may be used to define nodal coordinates, to indicate the principal axes for orthotropic materials, and to define the local axes for some elements.
		Some coordinate systems (such as element local surface coordinate systems) are determined by the element geometry and cannot be defined or modified by you.
		This section describes those coordinate systems that can be manipulated by a user to make data entry more convenient.
	www.iti-cae.com /caelabs/user_guide/stresslab/stresslab-414.html (162 words)

	A Spectral Method for Unbounded Flow in a Cylindrical Coordinate System - Shi, Wu (ResearchIndex) (Site not responding. Last check: 2007-10-09)
		Abstract: Fourier expansions in the radial direction for unbounded flows expressed in a cylindrical coordinate system are proposed.
		By appropriate coordinate mapping and periodic extension in the r direction, periodic boundary conditions required by Fourier expansions and infinite differentiability demanded by spectral convergence are established.
		Appropriate zero factors for the general Fourier expansions are given at the axis and at infinity in order to remove the numerical singularity at r = 0 and to...
	citeseer.ist.psu.edu /130928.html (410 words)

	PERBC2D (Site not responding. Last check: 2007-10-09)
		= 1 or 2, the constant coordinate location is the global Cartesian coordinate system [CSYS,0] location in the X or Y direction respectively.
		= 0, the coordinate location is the radial coordinate value in the global cylindrical coordinate system.
		The macro is restricted to node pairs sharing common coordinate values along symmetry planes separated by a constant coordinate value.
	www.oulu.fi /atkk/tkpalv/unix/ansys-6.1/content/Hlp_C_PERBC2D.html (432 words)

	Pro/ENGINEER Forum: Sinusoidal curve through equation
		• Theta (angle from y axis of coordinate system) - spherical coordinate system.
		• z (distance in z from coordinate system) - cylindrical coordinate system and Cartesian coordinate system.
		When using the spherical coordinate system, the results can be amazing.
	www.mcadcentral.com /proe/forum/forum_posts.asp?TID=21908 (448 words)

	Equation of motion for a particle: Newton’s 2nd law
		Equations of motion in a rectangular coordinate system: In a rectangular coordinate system the equations of motion can be represented by three scalar equations:
		Equations of motion in normal and tangential (natural) coordinate systems: In a natural coordinate system the equations of motion can be represented by three scalar equations:
		Equations of motion in Cylindrical coordinate systems: In a cylindrical coordinate system the equations of motion can be represented by three scalar equations:
	em-ntserver.unl.edu /NEGAHBAN/EM373/note9/note.htm (250 words)

	page17/htm (Site not responding. Last check: 2007-10-09)
		Spheroidal coordinates are obtained from a family of confocal ellipses and the associated family of confocal hyperbolas which are everywhere orthogonal to the ellipses.
		Prolate spheroidal coordinates are obtained by rotating the 2-dimensional system about the major axis of the ellipses, giving a family of elongated ellipsoids and an orthogonal family of hyperboloids of two sheets.
		may be taken to be the same as in the cylindrical system.
	www.lago.demon.co.uk /page17.htm (370 words)

	Mesh Building (Site not responding. Last check: 2007-10-09)
		One of the most effective uses of local coordinate systems is in manual or semi-automatic mesh building.
		In this example, calculation of the needed coordinates in the global Cartesian system would be a major task.
		However, by creating a local cylindrical coordinate system at the center of the circle, and declaring this system to be the Definition System for the new nodes, you can enter the needed coordinates directly in a fraction of the time.
	www.iti-cae.com /caelabs/user_guide/thermalab/thermalab-371.html (97 words)

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