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catenary

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catenary
catenary, n. and a. (kəˈtiːnərɪ) [ad. L. catēnāri-us relating to a chain, f. catēna chain.] A. n. Math. [mod.L. catenaria.] The curve formed by a chain or rope of uniform density hanging freely from two fixed points not in the same vertical line. The common catenary is the curve so formed by a chain... Oxford English Dictionary
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Catenary (disambiguation)
Catenary may refer to: Catenary, a mathematical curve Catenary arch, an arch that follows a catenary curve Catenary ring, a type of mathematical ring Overhead catenary, another name for the overhead line system for electric power transmission for railways wikipedia.org
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Is the catenary the trajectory of anything? Notice that the parabola, defined by certain properties, is also the trajectory of a cannon ball. Does the same sort of thing hold for the catenary? That is, is the catenary...
description here]( (image from Wikipedia) I'm not exactly sure how to frame this as a trajectory problem, but certainly there is stuff moving and a catenary Throughout a given quarter rotation starting with a vertex of the square at the bottom, the point directly below the radius will trace out an inverted catenary
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Catenary Nunatak
Catenary Nunatak () is a nunatak located southwest of Monastery Nunatak on the south side of the Quartermain Mountains, Victoria Land, in the Antarctic It is one of a group of names derived from terms used in surveying - a catenary being the curve in which a survey chain hangs when it is suspended between wikipedia.org
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Catenary arch
A catenary arch is a type of architectural arch that follows an inverted catenary curve. building More on the catenary, used in arches A few catenary arches An experiment A youtube, all about catenary arches A second youtube a youtube wikipedia.org
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Catenary Equation of a plane (3D) A catenary equation models a curve supported by two points, when solely acted on by gravity. The common formula is given as $y= a \cosh(\frac{x}{a})$ where $a$ is a constant regulat...
If you are looking for the equation of the surface generated by the rotation of a catenary around its axis of symmetry (taken as $z$ axis), then it is
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Catenary ring
universally catenary. A ring that is catenary but not universally catenary It is delicate to construct examples of Noetherian rings that are not universally catenary. wikipedia.org
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Evolute of a Catenary Ref of evolute of catenary Evolute of a Tractrix is a Catenary. What is the evolute of a Catenary? Sketched by Leonardo DaVinci Page 3, Fig 2. EDIT1: and also on Page 23, Fig 8. DaVinci_Last...
If you take the simplest case ($a=1$), the catenary is $\alpha(t)=(t,\cosh t)$. Catenary Evolute
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Weighted catenary
A weighted catenary is a catenary curve, but of a special form. A "regular" catenary has the equation for a given value of a. A weighted catenary is needed. wikipedia.org
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Proof that the polynomial ring over a field is catenary. Let $K$ be a field, $A=K[X_1,\dots,X_n]$. The following well known theorem shows $A$ is catenary; > _Every Cohen-Macaulay ring is catenary._ However, I want ...
There is a proof in Chapter 13 of Eisenbud's Commutative Algebra with a view toward algebraic geometry. The first part is a slight strengthening of the Noether Normalisation Lemma (Eisenbud's Theorem 13.3), but then to show that all maximal chains of primes have the same length, one also needs the G...
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USCGC Catenary
USCGC Catenary (WYTL-65606) was a cutter in the United States Coast Guard (USCG). On 1 May 1995, Catenary was decommissioned and sold to the United States Merchant Marine Academy. wikipedia.org
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English to Chinese Dictionary - Meaning of Catenary in Chinese is : 链状 ...
Catenary: Chinese Meaning: 链状, 链状的, 链状物; 悬链线; 悬垂线; 电气火车 the curve theoretically assumed by a perfectly flexible and inextensible cord of uniform density and cross section hanging freely from two fixed points / Alt. of Catenarian / a curve formed by a wire, rope, or chain hanging freely from two points and forming a U shape.,
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Is a Noetherian normal local domain (universally) catenary? Let $R$ be a ring. Then $R$ is $\textit{catenary}$ if for a pair of prime ideal $p \subseteq q$, all maximal chains of prime ideals $p = p_0 \subseteq p_1 \s...
There is a counter-example due to Ogoma in "Non-catenary pseudo-geometric normal rings", which seems to be a modification of one of Nagata's examples of a non-catenary ring.
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CN101010535A - Lightweight catenary system - Google Patents
A lightweight catenary system for deepsea operations in which a lightweight flexible pipe such as disclosed in U.S. Patent No. 6,491,779 is suspended in seawater from a vessel or platform, and having a positive or nearly positive buoyancy, and which is stabilized by disposing weight in proximity to or attached to the lower portion of the pipe at or near the seabed, whereby the weight and costs ...
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Research advances in electric contact between pantograph and catenary
Abstract. In recent years, with the improvement of running speed and current density of train, the electric contact status between pantograph and catenary is becoming more and more complex, which ...
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