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- A catenary is a curve that describes the shape of a flexible hanging chain or cable12. It is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform gravitational field1. Any freely hanging cable or string assumes this shape, also called a chainette, if the body is of uniform mass per unit of length and is acted upon solely by gravity2. The curve is assumed approximately by a heavy uniform cord or chain hanging freely from two points not in the same vertical line3.
Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.In physics and geometry, a catenary (US: / ˈkætənɛri / KAT-ən-err-ee, UK: / kəˈtiːnəri / kə-TEE-nər-ee) is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform gravitational field.en.wikipedia.org/wiki/Catenarycatenary, in mathematics, a curve that describes the shape of a flexible hanging chain or cable—the name derives from the Latin catenaria (“chain”). Any freely hanging cable or string assumes this shape, also called a chainette, if the body is of uniform mass per unit of length and is acted upon solely by gravity.www.britannica.com/science/catenaryCatenary definition: the curve assumed approximately by a heavy uniform cord or chain hanging freely from two points not in the same vertical line.www.dictionary.com/browse/catenary - People also ask
- nouncatenary (noun) · catenaries (plural noun)
- a curve formed by a wire, rope, or chain hanging freely from two points and forming a U shape:"a catenary wire"
- a wire, rope, or chain forming a catenary:"a catenary from the electrical grid"
Originmid 18th century: from Latin catenarius ‘relating to a chain’, from catena ‘chain’. - See more
See all on WikipediaCatenary - Wikipedia
In physics and geometry, a catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform gravitational field. The catenary curve has a U-like shape, superficially similar in appearance to a parabola, which it is not. The curve … See more
The word "catenary" is derived from the Latin word catēna, which means "chain". The English word "catenary" is usually attributed to Thomas Jefferson, who wrote in a letter to See more
In free-hanging chains, the force exerted is uniform with respect to length of the chain, and so the chain follows the catenary curve. The same is true of a simple suspension bridge or … See more
The catenary produced by gravity provides an advantage to heavy anchor rodes. An anchor rode (or anchor line) usually consists of chain or … See more
Model of chains and arches
In the mathematical model the chain (or cord, cable, rope, string, etc.) is idealized by assuming that it is so thin that it can be regarded as a curve and that it is so flexible any force of tension exerted by the chain is parallel to … See moreCatenary arches are often used in the construction of kilns. To create the desired curve, the shape of a hanging chain of the desired dimensions is transferred to a form which is then used … See more
Equation
The equation of a catenary in Cartesian coordinates has the form
See moreNonuniform chains
If the density of the chain is variable then the analysis above can be adapted to produce equations for the curve given the density, or given the curve to find the density.
Let w denote the … See moreWikipedia text under CC-BY-SA license Catenary | Mathematics, Physics & Engineering
WEBCatenary, in mathematics, a curve that describes the shape of a flexible hanging chain or cable—the name derives from the Latin catenaria (“chain”). Any freely hanging cable or string assumes this shape, also …
Equation of Catenary
WEBThe catenary is a plane curve, whose shape corresponds to a hanging homogeneous flexible chain supported at its ends and sagging under the force of gravity. The catenary …
Catenary -- from Wolfram MathWorld
WEB5 days ago · If you roll a parabola along a straight line, its focus traces out a catenary. As proved by Euler in 1744, the catenary is also the curve which, when rotated, gives the surface of minimum surface area (the catenoid) …
The Catenary (hanging chain), how it was first solved. - YouTube
The Catenary: Definition and Derivation - YouTube
Catenary Definition & Meaning - Merriam-Webster
WEBThe meaning of CATENARY is the curve assumed by a cord of uniform density and cross section that is perfectly flexible but not capable of being stretched and that hangs freely …
Maths in a minute: The catenary | plus.maths.org
WEBDec 5, 2016 · When you suspend a chain from two hooks and let it hang naturally under its own weight, the curve it describes is called a catenary. Any hanging chain will naturally find this equilibrium shape, in which the …
1. Introductory Statics: the Catenary and the Arch
WEBThe Catenary. What is the shape of a chain of small links hanging under gravity from two fixed points (one not directly below the other)? The word catenary (Latin for chain) was coined as a description for this curve by …
Catenary Definition (Illustrated Mathematics Dictionary) - Math is …
WEBIllustrated definition of Catenary: A curve made by a cable or chain when supported at its ends.
19.3: The Catenary - Physics LibreTexts
WEBConsider a chain elevated above ground, attached only at its two ends, both ends at the same height, and hanging under its own weight. The chain will sag, forming a hyperbolic …
Let’s Derive The Catenary Equation With Calculus - Medium
WEBNov 19, 2021 · A catenary (derived from the Latin catenaria meaning “chain”) is an idealized curve in physics or maths that represents the shape that a chain (or rope) …
18: The Catenary - Physics LibreTexts
WEBIf a flexible chain or rope is loosely hung between two fixed points, it hangs in a curve that looks a little like a parabola, but in fact is not quite a parabola; it is a curve called a …
Catenary Curve Calculator
WEBMay 21, 2024 · Suspended ropes have a simple yet fascinating mathematical definition: discover it with our catenary curve calculator! The catenary curve is the graph …
1.1: The Catenary - Physics LibreTexts
WEBDec 30, 2020 · Despite the image the word brings to mind of a chain of links, the word catenary is actually defined as the curve the chain approaches in the limit of taking …
WEBIf a flexible chain or rope is loosely hung between two fixed points, it hangs in a curve that looks a little like a parabola, but in fact is not quite a parabola; it is a curve called a …
WEBThe Catenary curve. Question: what is the shape of the St. Louis Gateway Arch? Not a parabola! New Question: find the shape of a hanging chain. 1. A mass hanging from two …
WEBCatenary is idealized shape of chain or cable hanging under its weight with the fixed end points. The chain (cable) curve is catenary that minimizes the potential energy. PHY …
What Is a Catenary System, and What Are Its Benefits?
WEBNov 30, 2022 · A catenary system is an overhead wire that supplies electricity to vehicles such as light rail trains and streetcars. Learn how it works, what are its …
18.3: Equation of the Catenary in Rectangular Coordinates, and …
WEBIf one end of the chain is fixed, and the other is looped over a smooth peg, Equation \( \ref{18.3.9}\) shows that the loosely hanging vertical portion of the chain just reaches the …
Derivation Catenary Equation With Calculus of Variations
WEBNov 19, 2021 · The Calculus of Variations is a mathematical tool we can use to find minima and maxima of functionals (loosely meaning function of a function in this context). …
Equation of Catenary - ProofWiki
WEBApr 19, 2024 · The catenary is described by the equation: y = eax +e−ax 2a = cosh ax a. where a is a constant. The lowest point of the catenary is at (0, 1 a).
Catenary - Types, Properties, Relation, Applications and Software …
WEB6 days ago · In Mathematics, a catenary is a curve that an idealized hanging chain or cable assumes when supported only at its ends under its own weight. The common …
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