Geodesy In geodesy , a referenceellipsoid is a mathematically defined surface that approximates the geoid ... the same referenceellipsoid. The longitude measures the rotational angle between the zero meridian ... that is Surface normal normal to the referenceellipsoid. Depending on the flattening, it may be slightly ..., and the height h of the point over the referenceellipsoid. If these coordinates, i.e., latitude ... the most common referenceellipsoid used, and that used in the context of the Global Positioning ... spheroid. For highly irregular bodies the concept of a referenceellipsoid may have no useful ... 0 GPS GPSHelmert1.html Coordinate Systems, Frames and Datums DEFAULTSORT ReferenceEllipsoid Category ... nl Referentie ellipso de pt Elipsoide de refer ncia ru simple Referenceellipsoid ..., reference ellipsoids are used as a preferred surface on which geodetic network computations are performed and point coordinates such as latitude , longitude , and elevation are defined. Ellipsoid parameters ... in equilibrium takes the form of an oblate ellipsoid of revolution which he termed an Oblate spheroid ... 1993 isbn 0 226 76747 7 page 82 ref uses the word ellipsoid alone in preference to the full term oblate ellipsoid of revolution or the older term oblate spheroid . In the rare instances some asteroid s and planet s where a more general ellipsoid shape is required as a model the term used is Triaxial ellipsoid triaxial or scalene ellipsoid. A great many ellipsoids have been used with various sizes ... or body being modeled. The shape of an oblate ellipsoid of revolution is determined by the shape parameters of that ellipse which generates the ellipsoid when it is rotated about its minor axis. The semi major axis of the ellipse, a , is identified as the equatorial radius of the ellipsoid the semi ... . These two lengths completely specify the shape of the ellipsoid but in practice geodesy publications classify reference ellipsoids by giving the semi major axis and the inverse flattening , 1 f , The flattening ... more details
, Cambridge, Mass. ISBN 978 0 674 03116 6. ref See also Paraboloid Hyperboloid Referenceellipsoid ...About the geometric three dimensional shape File Triaxial Ellipsoid.jpg thumb Tri axial ellipsoid with distinct semi axes lengths math c b a math File Ellipsoid tri axial abc.svg thumb 200px Tri axial ellipsoid with distinct semi axes a , b and c File Ellipsoid revolution prolate and oblate aac.svg thumb ... axis c which is an axis of symmetry. The ellipsoid is oblate or prolate as c is less than or greater than a . An ellipsoid is a closed Quadric quadric surface that is a three dimensional analogue of an ellipse . The standard equation of an ellipsoid centered at the origin of a Cartesian coordinate ... axial or rarely scalene ellipsoid math a b c math oblate ellipsoid of revolution oblate spheroid math a b c math prolate ellipsoid of revolution prolate spheroid math a b c math the degenerate case of a sphere Mathematical literature often uses ellipsoid in place of tri axial ellipsoid . Scientific literature particularly geodesy often uses ellipsoid in place of ellipsoid of revolution and only applies ... of ellipsoid of revolution . Any planar Cross section geometry cross section passing through the center of an ellipsoid forms an ellipse on its surface this degenerates to a circle for sections normal to the symmetry axis of an ellipsoid of revolution or all sections when the ellipsoid degenerates to a sphere. Generalised equations More generally, an arbitrarily oriented ellipsoid, centered at v ... directions of the ellipsoid and the eigenvalue s of A are the squares of the semi axes math a 2 math ... an ellipsoid, which can be brought into the above standard form by a suitable rotation , a consequence ... due to the spectral theorem and represent the directions of the axes of the ellipsoid the lengths ... of the ellipsoid may be parameterized in several ways. One possible choice which singles out ... of an ellipsoid is given by the formula math V frac 4 3 pi abc frac 4 3 pi sqrt det A . , math ... more details
Wiktionary latitude Ellipsoid may refer to Ellipsoid , a three dimensional geometrical shape. Referenceellipsoid for the shape of the Earth. Ellipsoidal reflector spotlight . disambig ... more details
nofootnotes date November 2009 one source date November 2009 The Hayford ellipsoid is a geodesy geodetic referenceellipsoid , named after the US geodesist John Fillmore Hayford 1868 1925 , which was introduced in 1910. The Hayford ellipsoid was also referred to as the International ellipsoid 1924 after it had been adopted by the International Union of Geodesy and Geophysics IUGG in 1924, and was recommended for use all over the world. Many countries retained their previous ellipsoids. The Hayford ellipsoid is defined by its semi major axis a 6,378,388.000 and its flattening f 1 297.00 . Unlike its predecessors, such as the Bessel ellipsoid a 6,377,397 m, f 1 299,15 , which was a European ellipsoid, the Hayford ellipsoid also included measurements from North America , as well as other continents to a lesser extent . It also included isostatic measurements to reduce plumbline divergences. It has since been replaced as the International ellipsoid by the newer Lucerne ellipsoid 1967 and GRS 80 1980 . Sources Defense Mapping Agency Geodesy for the layman , 1983, p. 8 http www.ngs.noaa.gov PUBS LIB Geodesy4Layman geo4lay.pdf Category Geodesy Category Geophysics de Hayford Ellipsoid ru ... more details
Unreferenced date February 2012 The Bessel ellipsoid or Bessel 1841 is an important referenceellipsoid of geodesy . It is currently used by several countries for their national geodetic surveys, in Europe and on other continents, but will be replaced in the next decades by modern ellipsoids of satellite geodesy . The Bessel ellipsoid was derived 1841 by Friedrich Wilhelm Bessel , based on several ... of network data. Every referenceellipsoid deviates from the worldwide data e.g. of satellite ... latitude and longitude see also Astro geodetic astro geodesy . The dimensions of the ellipsoid axes ... The Bessel ellipsoid fits especially well to the geoid curvature of Europe and Eurasia . Therefore ... 700 m shorter than that of the mean Earth ellipsoid derived by satellites. Below the are the two ... and the Global Positioning System GPS system. Bessel ellipsoid 1841 defined by log a and a 6,377,397.155 m 1 299.152815 3513233 0.003342 773154 0.000005 b 6,356,078.963 m . Earth ellipsoid WGS84 defined directly by a and a 6,378,137.0 m 1 298.257223563 b 6,356,752.30 m . Usage The ellipsoid ... to the Clarke ellipsoid of 1880. After the arrival of the geophysical reduction techniques many projects used other examples such as the Hayford ellipsoid of 1910 which was adopted in 1924 by the International Association of Geodesy IAG as the International ellipsoid 1924. All of them are influenced ... networks and about 20 of other continent s networks were based on the Bessel ellipsoid. In the following decades the Americas American states switched mainly to the Hayford ellipsoid 1908 internat ... after World War II. Russia forced its satellite states in Eastern Europe to use the Krassowski ellipsoid of about 1940. As of 2010 the Bessel ellipsoid is the geodetic system for Germany , for Austria ... coordinate system UTM coordinates Category Geodesy de Bessel Ellipsoid fr Ellipso de de Bessel nl Ellipso de van Bessel ru sv Bessels ellipsoid ... more details
math infty math where does this one go?? Mean Earth ellipsoid and reference ellipsoids A data set which describes the global average of the Earth s surface curvature is called the mean Earth Ellipsoid ... IUGG usually adopts the axes of the Earth ellipsoid to the best available data. See also Referenceellipsoid ... 2011 An Earth ellipsoid is a mathematical figure approximating the figure of the Earth shape of the Earth , used as a frame of referencereference frame for computations in geodesy, astronomy and the geosciences. Various different ellipsoids have been used as approximations. It is an ellipsoid of rotation ... poles is approximately aligned with the rotation axis of the Earth. The ellipsoid is defined by the equatorial ... of an Earth ellipsoid, ranging from meridian arc s up to modern satellite geodesy or the analysis ... survey s are several of special importance the Bessel ellipsoid of 1841, the international Hayford ellipsoid of 1924, and for GPS positioning the WGS84 ellipsoid. Historical Earth ellipsoids The following ... 6,356,256.913224 299.3249646 Bessel ellipsoid Bessel 1841 6,377,397.155 6,356,078.963 299.1528128 ... 6,378,200.0 close to WGS84 298.30 International Ellipsoid International 1924 6,378,388.0 6,356,911.9 297.0 SK 42 Reference System Krassowski 1940 6,378,245.00 for Eastern Europe 298.3 Internat. 1967 ... of the geoid . The latter is close to the mean sea level , and therefore an ideal Earth ellipsoid has the same volume as the geoid. While the mean Earth ellipsoid is the ideal basis of global geodesy, for regional networks a so called referenceellipsoid may be the better choice. When geodetic measurements have to be computed on a mathematical reference surface, this surface should have a similar ... would get small distortions. This is the reason for the long life of former reference ellipsoids like the Hayford ellipsoid Hayford or the Bessel ellipsoid , despite of the fact that their main axes ... s of millions of boundary stones should remain fixed for a long period. If their reference ... more details
Unreferenced date December 2009 In optics , an index ellipsoid is a diagram of an ellipsoid that depicts the orientation and relative magnitude of refractive index refractive indices in a crystal . The equation for the ellipsoid is constructed using the electric displacement field electric displacement vector D and the dielectric constant s. Defining the field energy W as math 8 pi W frac D 2 1 varepsilon 1 frac D 2 2 varepsilon 2 frac D 2 3 varepsilon 3 . math and the reduced displacement as math R i frac D i sqrt 8 pi W , math then the index ellipsoid is defined by the equation math frac R 1 2 varepsilon 1 frac R 2 2 varepsilon 2 frac R 3 2 varepsilon 3 1. math The semiaxes of this ellipsoid are dielectric constants of the crystal. This ellipsoid can be used to determine the Polarization waves polarization of an incoming wave with wave vector math vec s math by taking the intersection of the plane math vec R cdot vec s 0 math with the index ellipsoid. The axes of the resulting ellipse are the resulting polarization directions. Indicatrix An important special case of the index ellipsoid occurs when the ellipsoid is an ellipsoid of revolution, i.e. constructed by rotating an ellipse around either the minor or major axis, when two axes are equal and a third is different. In this case, there is only one optical axis, the axis of rotation, and the material is said to be uniaxial . When all axes of the index ellipsoid are equal, the material is isotropic . In all other cases, in which the ellipsoid has three distinct axes, the material is called biaxial . DEFAULTSORT Index Ellipsoid Category Optics Category Surfaces de Indexellipsoid nl Indicatrix sl Opti na indikatrisa ... more details
In robotics , the manipulability ellipsoid is the geometric interpretation of the scaled eigenvector s resulting from the singular value decomposition of the jacobian that describes a robot s motion. Category Robot control Category Geometry robotics stub ... more details
axis frame, it must lie on an ellipsoid , called inertia ellipsoid . The ellipsoid axes values are the half of the principal moments of inertia . The path traced out on this ellipsoid by the angular ... of applied torques, the angular momentum vector math mathbf L math is conserved in an inertial reference ... condition and construction These two constraints operate in different reference frames the ellipsoidal ... L math Hence, the normal vector to the kinetic energy ellipsoid at math boldsymbol omega math ..., these results show that, in an absolute reference frame, the instantaneous angular velocity vector ... energy ellipsoid that is tangent to it and rolls around on it without slipping. This is Poinsot ... energy constrains math mathbf L math to lie on an ellipsoid, whereas the angular momentum constraint ... more details
Ellipsoid Hill coord 77 48 S 163 50 E source GNIS is a rounded, partly ice covered summit, convert 1,130 m 2 high, to the north of Blue Glacier Antarctica Blue Glacier , between Geoid Glacier and Spheroid Hill , in Victoria Land , Antarctica. The name is one of a group in the area associated with surveying applied in 1993 by the New Zealand Geographic Board , and is for ellipsoid , in geodesy a mathematical figure formed by revolving an ellipse about its minor axis. ref name gnis References Reflist refs ref name gnis cite gnis type antarid id 4448 name Ellipsoid Hill accessdate 2012 02 29 ref usgs gazetteer id 4448 Category Hills of Victoria Land Category Scott Coast ScottCoast geo stub ... more details
File Chloryl hexafluoroantimonate xtal 2008 Cl coordination CM 3D ellipsoids.png thumb right 200px A thermal ellipsoid model of the coordination environment of the chlorine atom in the crystal structure of chloryl chloryl hexafluoroantimonate , ClO sub 2 sub SbF sub 6 sub , showing F Cl interactions. Thermal ellipsoids , more formally termed atomic displacement parameters , are ellipsoid s used in crystallography to indicate the magnitudes and directions of the thermal vibration of atom s in crystal structure s. Since the vibrations are usually anisotropic different magnitudes in different directions in space , an ellipsoid is a convenient way of visualising the vibration and therefore the time averaged position of an atom in a crystal. Thermal ellipsoids can be defined by a tensor , a mathematical object which allows the definition of magnitude and orientation of vibration with respect to Cartesian coordinate system three mutually perpendicular axes . The three principal axes of the thermal vibration of an atom are denoted math U 1 math , math U 2 math , and math U 3 math , and the corresponding thermal ellipsoid is based on these axes. The size of the ellipsoid is scaled so that it occupies the space in which there is a particular probability of finding the electron density of the atom. The particular probability is usually 50 . ref Massa2nd pages 35 37 ref See also Debye Waller factor References reflist Category Crystallography ... more details
In mathematics , the John ellipsoid E K associated to a convex body K in n dimension al Euclidean space R sup n sup is the ellipsoid of maximal n dimensional volume contained within K . The John ellipsoid is named after the Germany German mathematician Fritz John . The following refinement of John s original theorem, due to Ball 1992 , gives necessary and sufficient conditions for the John ellipsoid of K to be the closed unit ball B of R sup n sup The John ellipsoid E K of a convex body K R sup n sup is B if and only if B K and there exists an integer m n and, for i 1, ..., m , real number s c sub i sub > 0 and unit vector s u sub i sub S sup n &minus 1 sup K such that math sum i 1 m c i u i 0 math and, for all x R sup n sup math x sum i 1 m c i x cdot u i u i . math See also Steiner inellipse , the special case of the John ellipsoid for a triangle References cite journal last Ball first Keith M. title Ellipsoids of maximal volume in convex bodies journal Geom. Dedicata volume 41 year 1992 issue 2 pages 241&ndash 250 issn 0046 5755 doi 10.1007 BF00182424 John, Fritz. Extremum problems with inequalities as subsidiary conditions . Studies and Essays Presented to R. Courant on his 60th Birthday , January 8, 1948, 187 204. Interscience Publishers, Inc., New York, N. Y., 1948. oclc 1871554 MR 30135 cite journal last Gardner first Richard J. title The Brunn Minkowski inequality journal Bulletin of the American Mathematical Society Bull. Amer. Math. Soc. N.S. volume 39 issue 3 year 2002 pages 355&ndash 405 electronic issn 0273 0979 doi 10.1090 S0273 0979 02 00941 2 Category Convex geometry Category Multi dimensional geometry geometry stub de John Ellipsoid ... more details
File Ellipsoid 2.png thumb 400px An iteration of the ellipsoid method In mathematical optimization , the ellipsoid ... specialized to solving feasible linear optimization problems with rational data, the ellipsoid method is an algorithm , which finds an optimal solution in a finite number of steps. The ellipsoid method ... a minimizer of a convex function . History The ellipsoid method has a long history. As an iterative ... Judin . As an algorithm for solving linear programming problems with rational data, the ellipsoid ... polynomial time solvability of linear programs. Following Khachiyan s work, the ellipsoid method was the only ... faster than the ellipsoid method in practice. Karmarkar s algorithm is also faster in the worst ... equality constraints of the form math h i x 0 math . We are also given an initial ellipsoid ..., we have a point math x k math at the center of an ellipsoid math mathcal E k left x in mathbb R n ... E k cap z g k 1 T z x k leq 0 . math We set math mathcal E k 1 math to be the ellipsoid of minimal volume containing the half ellipsoid described above and compute math x k 1 math . The update ... Rightarrow f x k f x leq epsilon. math border 1 Sample sequence of iterates File Ellipsoid 1.png thumb center 250px math k 0 math File Ellipsoid 2.png thumb center 250px math k 1 math File Ellipsoid 3.png thumb center 250px math k 2 math File Ellipsoid 4.png thumb center 250px math k 3 math File Ellipsoid 5.png thumb center 250px math k 4 math File Ellipsoid 6.png thumb center 250px math k 5 math ... minimization, we have a point math x k math at the center of an ellipsoid math mathcal E k math as before ..., update the ellipsoid with a feasibility cut. Our feasibility cut may be a subgradient math g j math ... math . Application to Linear Programming Performance The ellipsoid method is used on low dimensional ..., it suffers from numerical instability and poor performance in practice. However, the ellipsoid ... theory , the ellipsoid algorithm is attractive because its complexity depends on the number ... more details
Refimprove date April 2010 pp move indef Reference is a relation between objects in which one object ... object refers is called the referent of the first object. The term reference is used in many spheres ... hide the reference from some observers, as in cryptography . The following sections give specific usages of reference in different subjects. Etymology The word reference is derived from ... science Main Reference computer science In computer science , Reference computer science reference ... of data structure s, such as linked list s. Generally, a reference is a value that enables a program to directly access the particular data item. Most programming language s support some form of reference. The C programming language has a specific type of reference also referred to as a reference see reference C . Bibliographies Bibliographies are special reference work s that are used to identify ... or researchers. Library and information sciences In a library , reference may refer to a dictionary , an encyclopedia or other reference work , that contains many brief articles that cover a broad scope of knowledge in one book, or a set of books. However, the word reference is also used to mean a book that cannot be taken from the room, or from the building. Many of the books in the reference department of a library are reference works, but some are books that are simply too large or valuable to loan out. Conversely, selected reference works may be shelved with other library circulation ... Resource Identifier URI . Librarians also conduct reference interview s at the library reference ... though virtual reference and digital reference services . Encyclopedias & books of facts Some published sources are produced as reference work s that allow quick access to essential information about .... Psychology In terms of mental processing, a self reference is used in psychology to establish ... own frames of reference in a greater state of immediate awareness. However, it can laso lead ... more details
Lame s stress ellipsoid Figure coming is an alternative to Mohr s circle for the graphical representation of the Stress mechanics Stress tensor stress state at a point . The surface of the ellipsoid represents the locus of the endpoints of all stress vectors acting on all planes passing through a given point in the continuum body. In other words, the endpoints of all stress vectors at a given point in the continuum body lie on the stress ellipsoid surface, i.e., the radius vector from the center of the ellipsoid, located at the material point in consideration, to a point on the surface of the ellipsoid is equal to the stress vector on some plane passing through the point. In two dimensions, the surface is represented by an ellipse Figure coming . Once the equations of the ellipsoid is known ... the equation of the stress ellipsoid we consider the coordinate axes math x 1, x 2, x 3 ... 2 2 2 frac T 3 sigma 3 2 2 1 , math which is the equation of an ellipsoid centered at the origin of the coordinate system, with the lengths of the semiaxes of the ellipsoid equal to the magnitudes of the principal stresses, i.e. the intercepts of the ellipsoid with the principal axes are math pm sigma ... to the sum of the principal radii of the ellipsoid. The second stress invariant math I 2 , math is directly proportional to the sum of the three principal areas of the ellipsoid. The tree principal ... proportional to the volume of the ellipsoid. If two of the three principal stresses are numerically equal the stress ellipsoid becomes an spheroid ellipsoid of revolution . ref name timoshenko1 ... stresses are equal and of the same sign, the stress ellipsoid becomes a sphere and any three perpendicular directions can be taken as principal axes. ref name timoshenko1 The stress ellipsoid ... vector of the stress ellipsoid acts on a plane oriented parallel to the tangent plane to the stress ... 0486611876 DEFAULTSORT Lame s Stress Ellipsoid Category Classical mechanics Category Materials science ... more details
Reference date may mean Reference date United States business cycles See Epoch reference date for information on dates used as reference points for calendars and time standards disambig ... more details
of reference in physics , may refer to a coordinate system or Cartesian coordinate system set of axes ... in it, or it may refer to an observational reference frame tied to the state of motion of an Observer special relativity observer . It may also refer to both an observational reference frame and an attached coordinate system as a unit. Different aspects of frame of reference The need to distinguish between the various meanings of frame of reference has led to a variety of terms. For example, sometimes the type of coordinate system is attached as a modifier, as in Cartesian frame of reference . Sometimes the state of motion is emphasized, as in Rotating reference frame rotating frame of reference ... frame of reference . Sometimes frames are distinguished by the scale of their observations, as in macroscopic and microscopic frames of reference . ref name macroscopic The distinction between macroscopic ... MicroAnalytix . ref In this article the term observational frame of reference is used when emphasis ... or observational apparatus. In this sense, an observational frame of reference allows study of the effect ... related to space and time. It seems useful to divorce the various aspects of a reference frame for the discussion below. We therefore take observational frames of reference, coordinate systems, and observational ... frame or non inertial frame of reference is a physical concept related to state of motion ... frame of reference can choose to employ any coordinate system Cartesian, polar, curvilinear, generalized, to describe observations made from that frame of reference. A change in the choice of this coordinate ... in the observer s observational frame of reference. This viewpoint can be found elsewhere as well ... books?id H3xIED8ctfUC&pg PA9&dq physical 22frame of reference 22 isbn 3540414436 year 2001 publisher Springer ref Cquote We first introduce the notion of reference frame , itself related to the idea of observer the reference frame is, in some sense, the Euclidean space carried by the observer ... more details
Reference frame may refer to Frame of reference , in physics Reference frame video , frames of a compressed video that are used to define future frames disambig ... more details
Point of reference is the intentional use of one thing to indicate something else. It may refer to Reference point General usage Frame of reference Physics usage disambig ... more details
Unreferenced date May 2009 In computer programming , a strong reference is a normal Reference computer science reference that protects the referred object from collection by a garbage collection computer science garbage collector . The term is used to distinguish the reference from weak reference s. Memory management navbox a Category Programming constructs Category Memory management compu lang stub ... more details
Refimprove date May 2009 A phantom reference is one of the strengths or levels of non strong reference strong reference defined in the Java programming language Java programming language the others being weak reference weak and soft reference soft . ref cite web title Package java.lang.ref url http docs.oracle.com javase 7 docs api java lang ref package summary.html work Java Platform, Standard Edition 7 API Specification publisher Oracle accessdate 12 December 2011 ref An object is phantomly referenced after it has been finalizer finalized , but before its allocated memory has been reclaimed. See also Weak reference Soft reference Circular reference References Reflist Category Programming constructs Category Memory management compu lang stub cs Phantom reference ... more details
Reference state is the intentional use of one thing to indicate something else. It may refer to Reference point General usage Standard state Chemistry usage disambig ... more details
A reference circuit is a hypothetical electric circuit of specified equivalent length and computer configuration configuration , and having a defined transmission characteristic or characteristics, used primarily as a reference for measuring the performance of other, i.e., real, circuits or as a guide for planning and engineering of circuits and networks. Normally, several types of reference circuits are defined, with different configurations, because Telecommunication communications are required over a wide range of distances. Another type of reference circuit shows how to configure integrated circuits into function blocks, which Analog Devices provides for electrical design engineers. Analog Devices Circuits from the Lab reference circuits are fully tested and come with the schematics, evaluation boards, and device drivers necessary for system integration. A group of related reference circuits is also called a reference system . References FS1037C MS188 See also netlist SPICE Category Electronic circuits ... more details
A soft reference is one of the strengths or levels of non strong reference strong reference defined in the Java programming language Java programming language , the others being weak reference weak and phantom reference phantom . The Garbage collection computer science garbage collector will always collect weakly referenced objects, but will only collect softly referenced objects when its algorithms decide that memory is low enough to warrant it. Soft and weak references provide two quasi priorities for non strongly referenced objects. Soft references may be used, for example, when writing a cache computing cache weakly referenced objects may disappear too quickly to make the cache useful. See also Weak reference Phantom reference Circular reference External links http www.pawlan.com monica articles refobjs Java developer article Reference Objects and Garbage Collection http weblogs.java.net blog enicholas archive 2006 05 understanding w.html Understanding Weak References Category Data types Category Memory management compu lang stub ... more details
Orphan date September 2010 The Reference 54 is a model of alto saxophone alto and tenor saxophone s, and part of the Selmer ReferenceReference series by musical instrument manufacturing company The Selmer Company Selmer . ref Cite web url http www.kesslermusic.com SelmerLeblanc referencesax.htm title Selmer Reference 54 & 36 Series Saxophones accessdate 17 May 2009 ref See also The Selmer Company References Reflist Woodwind instrument stub Category Musical instrument manufacturing companies Category Saxophones ... more details
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