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The word catenary is derived from the Latin word for "chain." The curve is also called the alysoid, funicular, and chainette. In 1669, Jungius disproved Galileo's claim that the curve of a chain hanging under gravity would be a parabola. The equation was obtained by Leibniz, Christiaan Huygens, and Johann Bernoulli in 1691 in response to a challenge by Jakob Bernoulli. Huygens was the first to use the term catenary in a letter to Leibniz in 1690, and David Gregory wrote a treatise on the catenary in 1690.
If you roll a parabola along a straight line, its focus traces out a catenary (see roulette (curve)). 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. Square wheels can roll perfectly smoothly if the road has evenly spaced bumps in the shape of a series of inverted catenary curves.
The intrinsic equation of the shape of the catenary is
In railway engineering, a catenary structure consists of overhead linesOverhead lines or overhead wires are used to transmit electrical energy to trams, trolleybusses, or trains at a distance from the energy supply point. These overhead lines are known variously as OCS overhead contact system US & Europe) OLE overhead line e or cables used to deliver electricity to a railway locomotiveA locomotive is a vehicle that provides the motive power for a railway train. Traditionally, the locomotive or locomotives are positioned at the front of a train, pulling passenger carriages and/or freight vehicles. This requires the locomotive to be move, multiple unitA multiple unit is a passenger train whose carriages have their own motors, (either diesel or electric) and do not need to be hauled by a locomotive. The motors driving the train on a multiple unit, are mounted underneath the floor of the carriages, on th, railcarNot to be confused with Railroad car A railcar is a self-propelled rail vehicle designed to transport passengers. The term 'Railcar' is usually used in reference to a train consisting of a single coach (carriage, car), with a drivers cab at each end., tramSirio low-floor tram in Athens, Greece passes in front of the Acropolis A tram (or tramway trolley streetcar strassenbahn is a light-rail vehicle for public transport. Trams are distinguished from other forms of light rail in that they travel along tracks or trolleybus through a pantographA pantograph (from Greek roots παν&tau 'all, every' and γρα&phi 'to write', from their original use for copying writing) is a series of arms connected in a special manner based on parallelograms so that they move in a fixed rel or sometimes a trolleypole . An alternative system is a third rail.
In structural engineering a catenary shell is a structural form,usually made of concrete, that follows a catenary curve. The profile for the shell is obtained by using flexible material subjected to gravity, converting it into a rigid formwork for pouring the concrete and then using it as required, usually in an inverted manner.
The Catalan architect Antoni Gaudí made extensive use of catenary shapes in his Sagrada Familia.
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