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The equation for this catenary with a as the y-intercept is y = a2 (ex/a + e-x/a).
n. pl. cat·e·nar·ies
1. The curve formed by a perfectly flexible, uniformly dense, and inextensible cable suspended from its endpoints. It is identical to the graph of a hyperbolic cosine.
2. Something having the general shape of this curve.
[New Latin catēnāria, from Latin, feminine of catēnārius, relating to a chain, from catēna, chain.]
n, pl -ries
1. (Mathematics) the curve assumed by a heavy uniform flexible cord hanging freely from two points. When symmetrical about the y-axis and intersecting it at y = a, the equation is y = a cosh x/a
2. (Railways) the hanging cable between pylons along a railway track, from which the trolley wire is suspended
3. (Civil Engineering) of, resembling, relating to, or constructed using a catenary or suspended chain
[C18: from Latin catēnārius relating to a chain]
cat•e•nar•y(ˈkæt nˌɛr i; esp. Brit. kəˈti nə ri)
n., pl. -nar•ies,
1. the curve assumed approximately by a heavy uniform cord or chain hanging freely from two points not in the same vertical line. Equation: y = k cosh (x/k).
2. (in electric railroads) the cable, running above the track, from which the trolley wire is suspended.adj.
3. of, pertaining to, or resembling a catenary.
[1780–90; < Latin catēnārius relating to a chain =catēn(a) a chain + -ārius -ary]