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Catenary - Wikipedia
In physics and geometry, a catenary (US: / ˈ k æ t ən ɛr i / KAT-ən-err-ee, UK: / k ə ˈ t iː n ər i / 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.orgCatenary -- from Wolfram MathWorld
5 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) for the given bounding circle. The parametric equations for the catenary are given by
Mathworld.wolfram.comEquation of Catenary
The 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 is similar to parabola (Figure 1).
Math24.netCatenary | Mathematics, Physics & Engineering | Britannica
catenary, 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 …
Britannica.comThe Catenary (hanging chain), how it was first solved. - YouTube
Oct 22, 2021 · The catenary is the mathematical shape of a hanging chain. Describing this shape is one of the famous original problems of calculus. I discuss the history of the problem, how it was determined
Youtube.comThe Catenary: Definition and Derivation - YouTube
A catenary is the mathematical curve formed by a uniform cable hanging under its own weight. Here, we give a complete derivation of the equation describing a
Youtube.com18.3: Equation of the Catenary in Rectangular Coordinates, and …
If one end of the chain is fixed, and the other is looped over a smooth peg, Equation 18.3.9 shows that the loosely hanging vertical portion of the chain just reaches the directrix of the catenary, and the tension at the peg is equal to the weight of the vertical portion.
Phys.libretexts.org18: The Catenary - Physics LibreTexts
If 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, which is a word derived from the Latin catena, a chain.
Phys.libretexts.org1.1: The Catenary - Physics LibreTexts
Dec 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 smaller and smaller links, keeping the length of the chain constant. In other words, it describes a hanging rope.
Phys.libretexts.orgCatenary Definition (Illustrated Mathematics Dictionary) - Math is …
Illustrated definition of catenary: A curve made by a cable or chain when supported at its ends.
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