Unreferenced date December 2009 Image DoubleCone.png thumb 250px right A circular conicalsurface In geometry , a general conicalsurface is the unbounded surface formed by the union of all the straight line mathematics lines that pass through a fixed point &mdash the apex or vertex &mdash and any point of some fixed space curve &mdash the directrix &mdash that does not contain the apex. Each of those lines is called a generatrix of the surface. Every conic surface is ruled surface ruled and developable surface developable . In general, a conicalsurface consists of two congruent unbounded halves joined by the apex. Each half is called a nappe , and is the union of all the Line mathematics Ray ..., the two nappes may intersect, or even coincide with the full surface. Sometimes the term conicalsurface is used to mean just one nappe. If the directrix is a circle math C math , and the apex ... to its plane , one obtains the right circular conicalsurface . This special case is often called ... conic section , and the apex is an arbitrary point not on the plane of math C math , one obtains a conical quadric , which is a special case of a quadric quadric surface . A cylindrical surface can be viewed as a limiting case of a conicalsurface whose apex is moved off to infinity in a particular direction. Indeed, in projective geometry a cylindrical surface is just a special case of a conicalsurface. Equations A conicalsurface math S math can be described parametrization parametrically as math ... circular conicalsurface of aperture math 2 theta math , whose axis is the math z math coordinate axis ... generally, a right circular conicalsurface with apex at the origin, axis parallel to the vector math ... given by math S x, y, z ax 2 by 2 cz 2 2uxy 2vyz 2wzx 0 math See also Conic section Quadric Ruled surface Developable surface DEFAULTSORT ConicalSurface Category Euclidean solid geometry Category Surfaces ... infty, infty math , respectively. In implicit geometric model implicit form, the same surface is described ... more details
follows the slope of the potential energy surface and reaches the conical intersection from above. At this point the very large vibronic coupling induces a non radiative transition surface hopping which ...Image PeakedCI.jpg thumb right Ideal Conical Intersection In quantum chemistry , a conical intersection of two potential energy surface s of the same spatial and spin symmetries is the set of molecular geometry points where the two potential energy surface s are degenerate intersect . Conical intersections are ubiquitous in both trivial and non trivial chemical systems. In a two coordinate system, this can occur at one molecular geometry . If the potential energy surfaces are plotted as functions of the two coordinates, they form a cone geometry cone centered at the degeneracy point. This is shown in the picture on the right, where the upper and lower potential energy surfaces are plotted in different colors. The name conical intersection comes from this observation. In a system with n coordinates, degenerate points lie in what is called the intersection space, or seam . The dimensionality of the seam is n 2. For a conical intersection, the remaining two dimensions that lift the energetic degeneracy of the system are known as the branching space. The conical intersections are also called molecular funnels or diabolic points . This comes from the very important role they play in non radiative de excitation transitions from excited electronic states to the ground electronic state of molecules. For example, the stability of DNA with respect to the UV irradiation is due to such conical ... to the topic of conical intersections in chemistry is Diabolical Conical Intersections , David Yarkony ... aspects of conical intersections can be found in Beyond Born Oppenheimer Electronic Nonadiabatic Coupling Terms and Conical Intersections by Michael Baer Wiley Interscience, 2006 . External links http ... webprojects2002 grant webcomp conical.html Potential Energy Surfaces and Conical Intersections Category ... more details
A conical mill or conical screen mill is a machine used to reduce the size of material in a uniform manner. It is an alternative to the hammermill or other forms of Mill grinding grinding mills . The conical mill operates by having the product being fed into the mill by gravity or vacuum. A rotating impeller forces the material outward to a conical screen surface, where it is sized and passed through the openings in the screen. Once finished, the product simply drops through the milling chamber to a receptacle underneath. Conical mills come in a variety of sizes from tabletop lab models to full size high capacity machines for use in processing large quantities of material, and the impeller and screen can be customized for each individual use. The machines can be used not only to reduce the size of particles, but also for deagglomeration, sieving, dispersion, and mixing. The applications for a conical mill are varied, but trend towards use in the food, cosmetic, chemical, and pharmaceutical ... . Creating breadcrumbs from scraps The conical mill has some marked advantages over the hammermill ... in design, and higher capacity. The concept of the conical mill was created in 1976 by the engineers of Quadro Engineering, who remain the foremost manufacturer of conical mills. Other companies such as L.B. Bohle have improved from the original conical mill concept and now offer equipment such as the BTS 100 & BTS 200 turbo conical mills with greater product throughput and excellent product ... cleaning. Sources http books.google.ca books?id AuK6R J2UFEC&pg PA187&lpg PA187&dq conical screen mill&source ... result&resnum 10&ct result Pharmaceutical Dosage Forms Details the advantages of conical mills in pharmaceutical ... Composition and Process for Preparing Describes how a conical mill works http www.informaworld.com smpp content content a786174010 db all Informa Healthcare review of a conical mill and its suitability ... 2008 month February pmid 17804181 doi 10.1016 j.ijpharm.2007.07.029 study of a conical mill s ability ... more details
In mathematics , conical functions or Mehler functions are function mathematics functions which can be expressed in terms of Legendre function s of the first and second kind, math P mu 1 2 i lambda x math and math Q mu 1 2 i lambda x . math The functions math P mu 1 2 i lambda x math were introduced by Gustav Ferdinand Mehler , in 1868, when expanding in series the distance of a point on the axis of a cone to a point located on the surface of the cone. Mehler used the notation math K mu x math to represent these functions. He obtained integral representation and series of functions representations for them. He also established an addition theorem for the conical functions. Carl Neumann obtained an expansion of the functions math K mu x math in terms of the Legendre polynomials in 1881. Leonhardt introduced for the conical functions the equivalent of the spherical harmonics in 1882. External links dlmf first T. M. last Dunster id 14.20 title Conical or Mehler Functions G. F. Mehler http www.digizeitschriften.de resolveppn GDZPPN002153386 Ueber die Vertheilung der statischen Elektricit t in einem von zwei Kugelkalotten begrenzten K rper Journal f r die reine und angewandte Mathematik 68 , 134 1868 . G. F. Mehler http www.digizeitschriften.de resolveppn GDZPPN002246112 Ueber eine mit den Kugel und Cylinderfunctionen verwandte Function und ihre Anwendung in der Theorie der Elektricit tsvertheilung Mathematische Annalen 18 p. 161 1881 . C. Neumann http www.digizeitschriften.de resolveppn GDZPPN002246120 Ueber die Mehler schen Kegelfunctionen und deren Anwendung auf elektrostatische Probleme Mathematische Annalen 18 p. 195 1881 . G. Leonhardt http www.digizeitschriften.de resolveppn GDZPPN002246694 Integraleigenschaften der adjungirten Kegelfunctionen Mathematische Annalen 19 p. 578 1882 . MathWorld title Conical function urlname ConicalFunction Milton Abramowitz ... the conical function P mu 1 2 i tau x SIAM J. Sci. Comput. 31 3 , 1716 1741 2009 . Category ... more details
Image Conical coordinates.png thumb 380px right Coordinate system Coordinate surface Coordinate surfaces of the conical coordinates. The constants b and c were chosen as 1 and 2, respectively. The red sphere represents r 2, the blue elliptic cone aligned with the vertical z axis represents cosh 1 and the yellow elliptic cone aligned with the green x axis corresponds to sup 2 sup 2 3. The three surfaces intersect at the point P shown as a black sphere with Cartesian coordinate system Cartesian coordinates roughly 1.26, 0.78, 1.34 . The elliptic cones intersect the sphere in taco shaped curves. Conical coordinates are a three dimensional orthogonal coordinates orthogonal coordinate system consisting of concentric spheres described by their radius math r math and by two families of perpendicular cones, aligned along the z and x axes, respectively. Basic definitions The conical coordinates math r, mu, nu math are defined by math x frac r mu nu bc math math y frac r b sqrt frac left mu 2 b 2 right left nu 2 b 2 right left b 2 c 2 right math math z frac r c sqrt frac left mu 2 c 2 right left nu 2 c 2 right left c 2 b 2 right math with the following limitations on the coordinates math nu 2 c 2 mu 2 b 2 math Surfaces of constant math r math are spheres of that radius centered on the origin math x 2 y 2 z 2 r 2 math whereas surfaces of constant math mu math and math nu math are mutually perpendicular cones math frac x 2 mu 2 frac y 2 mu 2 b 2 frac z 2 mu 2 c 2 0 math math frac x 2 nu 2 frac y 2 nu 2 b 2 frac z 2 nu 2 c 2 0 math In this coordinate system, both Laplace s equation and the Helmholtz equation are separable. Scale factors The scale factor for the radius math r math is one math h r 1 math , as in spherical coordinates . The scale factors for the two conical coordinates ... pages 118 119 id ASIN B000MBRNX4 cite book author Moon P, Spencer DE year 1988 chapter Conical Coordinates ... MathWorld description of conical coordinates Orthogonal coordinate systems Category Coordinate ... more details
alpha i ge 0. math The name derives from the fact that a conical sum of vectors defines a cone geometry cone possibly in a lower dimensional subspace . Conical hull The set of all conical combinations for a given set S is called the conical hull of S and denoted cone S , ref name conv an or coni ... point origin mathematics origin belongs to all conical hulls. The conical hull of a set S is a convex ... to see that a conical combination is a convex combination scaled by a positive factor. Image Circle conic hull.svg thumb right In the plane, the conical hull of a circle passing through the origin is the open ..., the conical combination and conical hull are more accurately to be called the convex conical combination and convex conical hull respectively. ref name conv an Moreover, the above remark about dividing the coefficients while discarding the origin implies that the conical combinations and hulls ... hull of a compact set is a compact set as well, this is not so for the conical hull first of all ... passing through the origin, with the conical hull being an open half space plus the origin. However if S is a nonempty compact set which does not contain the origin, the conical hull is a closed set. ref name conv an See also Related combinations details Linear combination Affine, conical, and convex ... more details
Refimprove date December 2009 A conical measure is a type of laboratory glassware which consists of a conical cup with a notch on the top to allow for the easy pouring of liquids, and graduated markings on the side to allow easy and accurate measurement of volumes of liquid. They may be made of plastic , glass , or Pyrex borosilicate glass . The use of the conical measure usually dictates its construction material. Plastic conical measures, commonly referred to as measuring cups are used by patients to measure liquid medicaments for oral administration. Glass and borosilicate conical measures are commonly used when compounding by the pharmacy profession. Conical measures are the most commonly used item of glassware used in the preparation of extemporaneous medicaments. They are not as precise as graduated cylinder s for measuring liquids, but make up for this in terms of easy pouring and ability to mix solutions within the measure itself. History During his experiment s, Ab al Rayh n al B r n 973 1048 invented the conical measure, ref Marshall Clagett 1961 . The Science of Mechanics in the Middle Ages , p. 64. University of Wisconsin Press . ref in order to find the ratio between the weight of a substance in air and the weight of water displaced, and to accurately measure the specific weights of the gemstones and their corresponding metal s, which are very close to modern measurements. fact date September 2011 References reflist Laboratory equipment DEFAULTSORT Conical Measure Category Volumetric instruments Category Laboratory glassware ar es Medida c nica fa simple Conical measure th ... more details
Conical drums are a class of membranophone , or drum , that is characterized by sloping sides. They are usually one headed. An example is the timbal . The conical drum also has strings on the side to keep the objest together. References cite web url http www.sil.org LinguaLinks Anthropology ExpnddEthnmsclgyCtgrCltrlMtrls mMembranophones.htm title 534m Membranophones work SIL accessdate January 4, 2007 Category Membranophones percussion instrument stub es Tambores c nicos ... more details
Unreferenced date December 2010 The Conical helmet was a helmet worn Citation needed date December 2010 by Illyrians , Adriatic Veneti Veneti , Celts and many of the Ancient peoples of Italy . It was in use from the 6th century BC. The helmet sometimes had a plume but not always. See also Illyrians Ancient Warfare References reflist commons Illyria & Illyrians DEFAULTSORT Conical Helmet Category Ancient helmets Category Ancient peoples of Italy Category Illyrian warfare ... more details
Geobox Range name Conical Range image image size image caption country Canada region British Columbia parent Pacific Ranges geology geology1 geology2 orogeny highest highest elevation highest lat d highest lat m highest lat s highest lat NS N highest long d highest long m highest long s highest long EW W map map size The Conical Range is a small mountain range in southwestern British Columbia , Canada , located between Seymour Inlet and Belize Inlet . ref BCGNIS 26782 Conical Range ref It has an area of 13 km sup 2 sup and is a subrange of the Pacific Ranges which in turn form part of the Coast Mountains . ref http www.bivouac.com ArxPg.asp?ArxId 1563 Conical Range in the Canadian Mountain Encyclopedia ref See also List of mountain ranges References reflist coord missing British Columbia Pacific Ranges Category Pacific Ranges BritishColumbiaCoast geo stub ... more details
For the hill in New Zealand Tapanui Branch distinguish Cone Hill Conical Hill coord 77 39 S 168 34 E source GNIS is a small but distinctive rock hill, convert 655 m 1 high, on the southern slopes of Mount Terror Antarctica Mount Terror , above Cape MacKay , on Ross Island . It was given this descriptive name by the British Antarctic Expedition, 1910 13 , under Robert Falcon Scott . References usgs gazetteer id 3041 Category Hills of Ross Island RossIsland geo stub ... more details
Conical Rock coord 62 43 S 61 11 W source GNIS is a rock lying in the eastern part of Morton Strait , convert 2 mi 0 south of the southwest tip of Livingston Island , in the South Shetland Islands . It was named by Discovery Investigations personnel on the RSS Discovery II Discovery II , who charted the area in 1930 31. References usgs gazetteer id 3042 Category Rock formations in Antarctica LivingstonIsland geo stub ... more details
Conical scanning is a system used in early radar units to improve their accuracy, as well as making it easier to steer the Antenna radio antenna properly to point at a target. Conical scanning is similar in concept to the earlier lobe switching concept used on some of the earliest radars, and many examples of lobe switching sets were modified in the field to conical scanning during World War II , notably the German W rzburg radar . With simple electronics, antenna guidance can be made entirely automatic ... of conical scan systems with monopulse radar sets. Concept A typical radar antenna commonly has ... motion. Conical Scanning Image Conical scan.jpg frame right Conical scanning concept. The radar beam .... Conical scanning addresses this problem by moving the radar beam slightly off center from the antenna ... width &ndash fairly typical &ndash a conical scanning radar might move the beam 1.5 degrees to one side ... within a degree or so in that maximum return area at the center of the lobe, with conical scanning ... the focal point of the paraboloid to produce the conical rotation. The other system is a nutated .... Basically conical scan of the non revolving nutating feed type , the size of the scan cone cyclically ... the target was acquired, the operator switched to conical scan for tracking. Since the lobe is being rotated around the midline of the antenna, conical scanning is only really appropriate for antennas ... in front of a passive reflector. To arrange conical scanning on such a system would require ... or weapons, can be added to a conical scan radar without too much trouble. The control system has ..., and dramatically change the amount of signal being returned. In these cases, a conical scan radar ... problems with all but impossibly fast changes in signal strength. Conical Scan Receive Only COSRO ... drive motors. Jamming Conical scan radars can be easily electronic warfare jammed . If the target ... , for Conical Scan on Receive Only compare to LORO , a similar system used against lobe switching ... more details
A conical pendulum is a weight or bob physics bob fixed on the end of a string or rod suspended from a pivot. Its construction is similar to an ordinary pendulum however, instead of rocking back and forth, the bob of a conical pendulum moves at a constant speed in a circle with the string or rod tracing out a cone geometry cone . The conical pendulum was first studied by the English scientist Robert Hooke around 1660 ref name Oconnor cite web last O Connor first J.J. authorlink coauthors E.F. Robertson title Robert Hooke work Biographies, http www groups.dcs.st and.ac.uk history MacTutor History of Mathematics Archive publisher School of Mathematics and Statistics, Univ. of St. Andrews, Scotland date August 2002 url http www groups.dcs.st and.ac.uk history Biographies Hooke.html doi accessdate 2009 02 21 ref as a model for the orbital motion of planet s. ref name Nauenberg cite conference first Michael last Nauenberg authorlink coauthors title Robert Hooke s seminal contribution to orbital dynamics booktitle Robert Hooke Tercentennial Studies pages 17 19 publisher Ashgate Publishing date 2006 location url http books.google.com books?id P0 XfTTcwwQC&pg PA3&lpg PA17&dq Nauenberg Robert hooke orbital seminal&source bl&ots zO22H8fKNA&sig 8s2F9CBhTetr28uvBeFuaEQoMik&hl en& doi id ISBN ...&pg PA15 date 1890 id accessdate 2008 02 25 ref Uses During the 1800s, conical pendulums were used ... disturb sleep. Conical pendulums had other uses unrelated to timekeeping. A pair of conical pendulums ... engines. Analysis Consider a conical pendulum consisting of a Bob physics bob of mass m revolving ... the center of the circle math T sin theta frac mv 2 r , math Image Conical pendulum.svg thumb right 250px Conical pendulum whose bob travels in a horizontal circle of radius r . The bob has mass m and is suspended ... t of a conical pendulum is equal to the period of an ordinary pendulum of the same length. Also ... wiki englishhtm ConicalPendulum.htm An interactive Java simulation of conical pendulum Category Pendulums ... more details
wiktionarypar surface dablink This article discusses surfaces from the point of view of topology . For other uses, see Differential geometry of surfaces , algebraic surface , and Surface disambiguation . Image Saddle pt.jpg thumb 225px right An open surface with X , Y , and Z contours shown. In mathematics , specifically in topology , a surface is a two dimensional topological manifold . The most familiar ... Euclidean space R sup 3 sup &mdash for example, the surface of a ball . On the other hand, there are surfaces ... space without introducing singularity theory singularities or self intersections. To say that a surface ... dimensional coordinate system is defined. For example, the surface of the Earth is ideally a two dimensional ... and along the 180th meridian . The concept of surface finds application in physics , engineering ... consideration is the flow of air along its surface. Definitions and first examples A topological surface is a nonempty Second countable space second countable Hausdorff space Hausdorff topological ... Euclidean . More generally, a topological surface with boundary is a Hausdorff space Hausdorff ... on the surface mapped via a chart to the x axis is termed a boundary point . The collection of such points is known as the boundary of the surface which is necessarily a one manifold, that is, the union ... . The collection of interior points is the interior of the surface which is always non empty set empty . The closed disk mathematics disk is a simple example of a surface with boundary. The boundary of the disc is a circle. The term surface used without qualification refers to surfaces without boundary. In particular, a surface with empty boundary is a surface in the usual sense. A surface with empty boundary which is compact is known as a closed surface. The two dimensional sphere, the two dimensional torus , and the real projective plane are examples of closed surfaces. The M bius strip is a surface with only one side . In general, a surface is said to be orientable if it does not contain ... more details
Image Wallis s conical edge.svg right thumb 350px Figure 1. Wallis s Conical Edge with a b c 1 Image Wallis Conical Edge.gif right thumb 600px Figure 2. Wallis s Conical Edge with a 1.01,b c 1 Wallis s conical edge is a ruled surface given by the parametric equations math x v cos u, quad y v sin u, quad z c sqrt a 2 b 2 cos 2u . , math where a , b and c are constants. Wallis s conical edge is also a kind of right conoid . Figure 2 shows that the Wallis s conical edge is generated by a moving line. Wallis s conical edge is named after the English mathematician John Wallis , who was one of the first to use Analytic geometry Cartesian methods to study conic sections . http books.google.com books?id owEj9TMYo7IC&pg PA450&lpg PA450&dq John Wallis 22conical edge 22&source bl&ots j591Txb0Li&sig GqlLD5QzHjtZwm67hVaDILWBoUE&hl en&ei kG5uSpWFHqj26gOD Ky5BA&sa X&oi book result&ct result&resnum 1 See also Ruled surface Right conoid External links http mathworld.wolfram.com WallissConicalEdge.html Wallis s Conical Edge from MathWorld. References A. Gray, E. Abbena, S. Salamon, Modern differential geometry of curves and surfaces with Mathematica , 3rd ed. Boca Raton, FL CRC Press, 2006. http www.crcpress.com ecommerce product product detail.jsf?catno C4487&isbn 0000000000000 ISBN 9781584884484 Category Surfaces Category Geometric shapes geometry stub ... more details
is n n l leaf hat . Among conical hats, n n l of Vietnamese has the most original geometric ... conical hats in Vietnam contain colourful hand stitch depictions or words while the Hu varieties are famous for their n n b i th literally poem conical hats . These contain random poetic verses ... switch of videogame joystick s was formerly known as coolie hat because of its resemblance to the conical ... References reflist External links Commons category Conical straw hats http www.fotopedia.com en Conical straw hat Conical straw hats gallery DEFAULTSORT Conical Straw Hat Category Hats Category ... more details
Image Ruled hyperboloid.jpg thumb right 400px A hyperboloid of one sheet is a doubly ruled surface it can be generated by either of two families of straight lines. In geometry , a surface S is ruled if through ... mathematics plane and the curved surface of a cylinder geometry cylinder or cone geometry cone . Other examples are a conicalsurface with ellipse elliptical directrix , the right conoid , the helicoid , and the tangent developable of a smooth curve in space. A ruled surface can always be described ... is formed by keeping one point of a line fixed whilst moving another point along a circle . A surface is doubly ruled if through every one of its points there are two distinct lines that lie on the surface ... is the only surface which contains three distinct lines through each of its points. The properties ... surface has a parametric equation parametric representation of the form math S t,u p t u r t math where math S t,u math is the generic point on the surface, math p t math is point that traces a curve lying on the surface, and math r t math is a unit vector unit length vector that traces a curve ... t cos 2 t , cos t sin 2 t, sin t end align math one obtains a ruled surface that contains the M bius strip . Alternatively, a ruled surface can be parametric model parametrized as math S t,u 1 u p t u q t math , where math p math and math q math are two non intersecting curves lying on the surface ... , the surface is a hyperbolic paraboloid , or a piece of an hyperboloid of one sheet. Developable surface A developable surface is a surface that can be locally unrolled onto a flat plane without tearing or stretching it. If a developable surface lies in three dimensional Euclidean space, and is complete ... generally, any developable surface in three dimensions is part of a complete ruled surface, and so ... on the surface through any given point, and this condition is now often used as the definition of a ruled surface ruled surfaces are defined to be abstract projective surfaces satisfying this condition ... more details
In mathematics , a developable surface is a surface with zero Gaussian curvature . That is, it is a surface that can be Flatness flattened onto a Plane mathematics plane without distortion i.e. stretching or compressing . Conversely, it is a surface which can be made by Transformation mathematics transforming a plane i.e. folding , bending , rolling , cutting and or gluing . In three dimensions all developable surfaces are ruled surface s. There are developable surfaces in R sup 4 sup which are not ruled. ref Citation last1 Hilbert first1 David author1 link David Hilbert last2 Cohn Vossen first2 Stephan author2 link Stephan Cohn Vossen title Geometry and the Imagination publisher Chelsea location New York edition 2nd isbn 978 0 8284 1087 8 year 1952 pages 341 342 ref Particulars The developable surfaces which can be realized in three dimensional space are ref James J. Stoker Stoker, J.J. 1961 , Developable surfaces in the large. Communications on Pure and Applied Mathematics Comm. Pure Appl. Math. 14 3 , 627 635, doi 10.1002 cpa.3160140333 ref Cylinder geometry Cylinder s and, more generally, the generalized cylinder its Cross section geometry cross section may be any smooth function smooth curve Cone geometry Cone s and, more generally, conicalsurface s away from the apex geometry apex Planes trivially which may be viewed as a cylinder whose cross section is a Line mathematics ... . Formally, in mathematics, a developable surface is a surface with zero Gaussian curvature . One consequence of this is that all developable surfaces embedded in 3D space are ruled surface s though ... surfaces can be Scientific visualization visualised as the surface formed by moving a straight ... to a developable surface and then unrolling the surface into a region on the plane. Since they may ... title Developable Surface http www.rhino3.de design modeling developable Examples of developable ... geometry of surfaces de Abwickelbare Fl che et Tasanduv pind fr Surface d veloppable ko ja ... more details
The surface to surface intersection SSI problem . is a basic problem in computer aided geometric design Given two intersecting surfaces in R sup 3 sup , compute all parts of the intersection curve. If two surfaces intersect, the result will be a set of isolated points, a set of curves, a set of overlapping surfaces, or any combination of these cases ref R. Barnhill, G. Farin, M. Jordan, and B. Piper. SurfaceSurface Intersection. Computer Aided Geometric Design, 4 3 16,1987. ref . Because exact solutions can be found only for some special surface classes, approximation methods must be used for the general case. References reflist External links http www.ads.tuwien.ac.at research ssi Surface to Surface Intersection Algorithms http ieeexplore.ieee.org xpls abs all.jsp?arnumber 180122 Surface to surface intersections N.M. Patrikalakis Further reading Ernst Huber, Intersecting General Parametric Surfaces Using Bounding Volumes, Tenth Canadian Conference on Computational Geometry CCCG 98,1998. Ernst Huber, Surface to surface intersection based on triangular parameter domain subdivision, Proceedings of the 11th Canadian Conference on Computational Geometry, UBC, Vancouver, British Columbia, Canada, August 15 18, 1999 Handbook of Computer Aided Geometric Design, By Gerald E. Farin, Josef Hoschek, Myung Soo Kim, Published by Elsevier, 2002, ISBN 0444511040, 9780444511041 Category Geometric algorithms Category Computer aided design ... more details
the inclination angle of conicalsurface. Figure 6 shows Mohr Coulomb yield surface in two dimensional ... space. A yield surface is a five dimensional surface in the six dimensional space of Stress mechanics stresses . The yield surface is usually convex polytope convex and the state of stress of inside the yield surface is elastic. When the stress state lies on the surface the material is said to have ... plastic . Further deformation of the material causes the stress state to remain on the yield surface, even though the shape and size the surface may change as the plastic deformation evolves. This is because stress states that lie outside the yield surface are non permissible in plasticity physics .... C. and Hughes, T,. J. R., 1998 , Computational Plasticity , Spinger. ref The yield surface is usually ... of the yield surface that is, the yield function in the forms math f sigma 1, sigma 2, sigma ... most popular are listed below. Tresca yield surface The Tresca yield criterion is taken to be the work ... S y math is the tensile yield strength. Figure 1 shows the Tresca Guest yield surface in the three ... the plastic domain. Figure 2 shows the Tresca Guest yield surface in two dimensional stress space ... Surface 3D.png left 400px thumb Figure 1 View of Tresca Guest yield surface in 3D space of principal stresses Image Tresca Guest Yield Surface 2D.png none 200px thumb Figure 2 Tresca Guest yield surface in 2D space math sigma 1, sigma 2 math von Mises yield surface main von Mises yield criterion ... tension. Figure 3 shows the von Mises yield surface in the three dimensional space of principal stresses ... angles to the three principal stresses. Figure 4 shows the von Mises yield surface in two dimensional ... of math sigma 1, sigma 2 math produces the ellipse elliptical shape of the yield surface. Image Mises Yield Surface 3D.png left 400px thumb Figure 3 View of Huber Mises Hencky yield surface in 3D space ... Guest and Huber Mises Hencky criteria in 2D space math sigma 1, sigma 2 math Mohr Coulomb yield surface ... more details
Molecular surface may refer to one of the following. the van der Waals surface Accessible surface area any of isosurface s for a molecule Connolly surface disambig ... more details
The Anterior surface can refer among other things the following anterior surface of pancreas anterior surface of cervical vertebrae disambig ... more details
Image Surface of revolution illustration.png thumb A portion of the curve x 2 cos z rotated around the z axis A surface of revolution is a surface in Euclidean space created by rotating a curve the generatrix around a straight line in its plane the axis . ref Analytic Geometry Middlemiss, Marks, and Smart. 3rd Edition Ch. 15 Surfaces and Curves, § 15 4 Surfaces of Revolution LCCN 68 015472 pp 378 ff. ref Examples of surfaces generated by a straight line are cylinder geometry cylindrical and conicalsurface s when the line is coplanar with the axis, as well as Hyperboloid hyperboloids of one sheet when the line is Skew lines skew to the axis. A circle that is rotated about a diameter generates a sphere and if the circle is rotated about a coplanar axis other than the diameter it generates a torus . Area formula If the curve is described by the parametric functions math x t math , math ..., Area of a Surface of Revolution pp 206 209, The Theorems of Pappus, pp 217 219 LCCN 69 016407 ref ... surface with unit radius is generated by the curve x t sin t , y t cos t , when t ranges over math ... a surface of revolution out of any 2 dimensional scalar function math y f x math , simply ... on a surface of revolution Geodesics on a surface of revolution are governed by Clairaut s relation ... be used to determine surface area without the use of measuring the length and radius of the object being designed. See also Channel surface , a generalisation of a surface of revolution Gabriel s Horn Liouville surface , another generalization of a surface of revolution Solid of revolution Surface integral References references External links MathWorld title Surface of Revolution urlname SurfaceofRevolution http www.mathcurve.com surfaces revolution revolution.shtml Surface de r volution at Encyclop die des Formes Math matiques Remarquables DEFAULTSORT Surface Of Revolution Category Integral ... de revoluci n fr Surface de r volution it Superficie di rotazione kk lv Rot cijas virsma ... more details
A surface to surface missile also known as, ground to ground missile , SSM or GTGM is a guided projectile launched from a hand held, vehicle mounted, trailer mounted or fixed installation or from a ship. They are often powered by a rocket rocket motor or sometimes fired by an explosive charge, since the launching platform is typically stationary or moving slowly. They usually have fins and or wings for lift and stability, although hyper velocity or short ranged missiles may utilise body lift or fly a ballistic trajectory. The V 1 flying bomb Fieseler Fi 103 also known as the V1 was the first surface to surface missile. Contemporary surface to surface missiles are usually guided. An unguided surface to surface missile is usually referred to as a rocket for example, an RPG 7 or M72 LAW is an anti tank rocket whereas a BGM 71 TOW or AT 2 Swatter is an anti tank guided missile . Surface to surface missiles are usually broken down into a number of categories Ballistic missile s travel in a high trajectory, motor burns out partway through flight Tactical ballistic missile Range between about 150 km and 300 km Battlefield Range Ballistic Missile Battlefield range ballistic missile BRBM Range less than 200 km Theatre ballistic missile TBM Range between 300 km and 3500 km Short range ballistic missile SRBM Range 1000 km or less Medium range ballistic missile MRBM Range between 1000 km and 3500 km Intermediate range ballistic missile IRBM or Intermediate range ballistic missile Long range ballistic missile LRBM Range between 3500 km and 5500 km Intercontinental ballistic missile ICBM Range greater than 5500 km Submarine launched ballistic missile SLBM Launched from ballistic missile submarine s SSBNs , all current designs have intercontinental range. Cruise missile s travel low to the ground, motor burns during entire flight ... SSM Category Surface to surface missiles bg de Boden Boden Rakete fr Missile sol ... more details
Encyclopedia
top
