Cleanup date August 2009 In geodesy , a referenceellipsoid is a mathematically defined surface that approximates .... Ellipsoid parameters Mathematically, a referenceellipsoid is usually an oblate flattened spheroid ... when defining a referenceellipsoid to specify the semi major equatorial radius math a , math ... normal normal to the referenceellipsoid. Depending on the flattening, it may be slightly different ... h of the point over the referenceellipsoid. If these coordinates, i.e., latitude math phi , math ... the concept of a referenceellipsoid may have no useful value, so sometimes a spherical reference ... Aerospace Blockset ECEF Position to LLA DEFAULTSORT ReferenceEllipsoid Category ... simplicity, reference ellipsoids are used as a preferred surface on which geodetic network computations ... pole polar radius the semi minor axis math b , math . More rarely, a scalene ellipsoid with three ... center of the ellipsoid is placed at the center of mass of the body being modeled, and not the Center ... use of reference ellipsoids is to serve as a basis for a coordinate system of latitude north ... Airy 0 . It is possible for many different coordinate systems to be defined upon the same referenceellipsoid. The longitude measures the rotational angle between the zero meridian and the measured ... from the center of the ellipsoid. For non Earth bodies the terms planetographic and planetocentric ... arctan left frac Y t X t right . , math Historical Earth ellipsoids Main Earth ellipsoid Historical Earth ellipsoids Figure of the Earth Historical Earth ellipsoids Currently the most common referenceellipsoid used, and that used in the context of the Global Positioning System, is WGS 84 . Traditional reference ellipsoids or geodetic datum s are defined regionally and therefore non geocentric ... Clarke 1866 6 378 206.4 6 356 583.8 294.978 698 2 Bessel ellipsoid Bessel 1841 6 377 397.155 6 356 078.965 299.152 843 4 International Ellipsoid International 1924 6 378 388 6 356 911.9 297 SK 42 ... 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 ... 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 Reference ...Unreferenced date February 2009 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 .... It is an ellipsoid of rotation, whose short polar axis connecting the two flattest spots called geographical north and south poles is approximately aligned with the rotation axis of the Earth. The ellipsoid ... of the axes of an Earth ellipsoid, ranging from meridian arc s up to modern satellite ... set of data used in national 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 ... 6,377,563.4 6,356,256.91 299.3249646 Bessel ellipsoid Bessel 1841 6,377,397.155 6,356,078.963 299.1528128 ... 1906 6,378,200.0 close to WGS84 298.30 International Ellipsoid International 1924 6,378,388.0 6,356,911.9 297.0 Krassowski ellipsoid 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
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 meridian arc s and other data of continental geodetic network s of Europe , Russia and the British Survey of India . It is based on 10 meridional arcs and 38 precise measurements of the astro geographic latitude and longitude see also Astro geodetic astro geodesy . The dimensions of the ellipsoid axes were defined by logarithm s in keeping with former calculation methods. The Bessel and GPS ellipsoids The Bessel ellipsoid fits especially ..., rock density and the distribution of network data. Every referenceellipsoid deviates from the worldwide ... that of the mean Earth ellipsoid derived by satellites. Below the two axes a , b and the flattening ... 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 data published by Bessel 1841 were ... all national surveys just some surveys in Asia switching to the Clarke ellipsoid of 1880. After ... ellipsoid of 1910 which was adopted in 1924 by the IAG as the International ellipsoid 1924 ... on the Bessel ellipsoid. In the following decades the Americas American states switched mainly to the Hayford ellipsoid 1908 internat. Ell. 1924 which was also used for the European unification project ... to use the Krassowski ellipsoid of about 1940. As of 2010 the Bessel ellipsoid is the geodetic system ... Geodesy de Bessel Ellipsoid fr Ellipso de de Bessel nl Ellipso de van Bessel ru sv Bessels ellipsoid ... 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 Optische Indikatrix nl Indicatrix sl Opti na indikatrisa ... more details
axis frame, it must lie on an ellipsoid , called inertia ellipsoid . math T frac 1 2 I 1 omega 1 2 frac 1 2 I 2 omega 2 2 frac 1 2 I 3 omega 3 2 math The ellipsoid axes values are the half of the principal moments of inertia . The path traced out on this ellipsoid by the angular velocity vector ... math mathbf L math is conserved in an inertial reference frame math frac d mathbf L dt 0 math . The angular ... 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 is proportional ... show that, in an absolute reference frame, the instantaneous angular velocity vector math ... energy ellipsoid that is tangent to it and rolls around on it without slipping. This is Poinsot s construction ... mathbf L math to lie on an ellipsoid, whereas the angular momentum constraint constrains math mathbf ... more details
orphan date February 2009 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 Robotics Category Geometry robotics stub ... more details
Ellipsoid Hill coor dm 77 48 S 163 49 E is a rounded, partly ice covered summit 1,130 m to the north of Blue Glacier , between Geoid Glacier and Spheroid Hill , in Victoria Land . The name is one of a group in the area associated with surveying applied in 1993 by New Zealand Geographic Board NZGB . Named from ellipsoid, in geodesy a mathematical figure formed by revolving an ellipse about its minor axis. usgs gazetteer Category Geography of Antarctica EAntarctica 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 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 MathSciNet 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 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 ... B. Yudin Judin . As an algorithm for solving linear programming problems with rational data, the ellipsoid ... time polynomial time solvability of linear programs. Following Khachiyan s work, the ellipsoid ..., the interior point method and variants of the simplex algorithm are much faster than the ellipsoid ... ellipsoid math mathcal E 0 subset mathbb R n math defined as math mathcal E 0 left z in mathbb R n ..., we have a point math x k math at the center of an ellipsoid math mathcal E k left x in mathbb ... x in mathcal 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 ... epsilon 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 ... minimization, we have a point math x k math at the center of an ellipsoid math mathcal E k ... constraint, update the ellipsoid with a feasibility cut. Our feasibility cut may be a subgradient math ... math z math . Application to Linear Programming Performance The ellipsoid method is used on low dimensional ... sized problems, it suffers from numerical instability and poor performance in practice. However, the ellipsoid ... complexity theory , the ellipsoid algorithm is attractive because its complexity depends on the row ... more details
Refimprove date April 2010 about help in citing references Wikipedia Citing sources the Wikipedia Reference Desk Wikipedia Reference desk Wiktionary A reference , is derived from Middle English referren ... from this root, including referee, reference, referendum , all retaining the basic meaning of the original ... reference is use in every sphere of human knowledge, adopting shades of meaning particular to the contexts ... form. This includes methods that intentionally hide the reference from some observers, as in cryptography . The following sections give specific usages of reference in different subjects. Knowledge ... science Main Reference computer science In computer science , Reference computer science reference ... variety of data structure s, such as linked list s. Generally, a reference is a value that enables ... of reference. Computer programming, programs & data Expand section date February 2011 The C programming language has a specific type of reference also referred to as a reference see reference C . Bibliographies Expand section date February 2011 Bibliographies are special reference work s that are used ... for other authors or researchers. Library & 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 ... Uniform Resource Identifier URI . Librarians also conduct reference interview s at the library reference ... though virtual reference and digital reference services . Encyclopedias & books of facts Expand section date February 2011 Some published sources are produced as reference work s that allow ... 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
A frame of reference in physics , may refer to a coordinate system or Cartesian coordinate system set ... of objects 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 ... of reference . Sometimes the state of motion is emphasized, as in Rotating reference frame rotating frame of reference . Sometimes the way it transforms to frames considered as related is emphasized as in Galilean 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 ... 2002 publisher MicroAnalytix . ref In this article the term observational frame of reference is used ... of the observations or observational apparatus. In this sense, an observational frame of reference ... indirectly 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 ... frame such as an inertial frame or non inertial frame of reference is a physical concept related to state ... in an observational 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 ... not entail a change in the observer s observational frame of reference. This viewpoint can be found ...&pg PA9&dq physical 22frame of reference 22&lr &as brr 0&sig ACfU3U1tEWQICZdsXeuLyfmH2PoLgZnMGA 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 ... 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 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 . 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 Category Programming constructs Category Memory management compu lang stub cs Phantom reference ... 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
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