CATENARY

the curve describing the shape taken by a homogeneous cable that is suspended by its endpoints. 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. The general equation of a catenary is y = a cosh (x/a), in which a is a constant, the distance between the lowest point of the curve and a reference axis. If a = 1, the equation is that of the hyperbolic cosine (cosh). The approximate curve may be observed in the cables of suspension bridges. The catenary can be generated as the locus of the focus of a parabola rolling along a straight line.