statics bsc 2nd year mathematics
11 videos • 197 views • by EBI SAMADHAN The catenary curve has a U-like shape, superficially similar in appearance to a parabolic arch, but it is not a parabola. The curve appears in the design of certain types of arches and as a cross section of the catenoid—the shape assumed by a soap film bounded by two parallel circular rings. The catenary is also called the alysoid, chainette,[1] or, particularly in the materials sciences, funicular.[2] Rope statics describes catenaries in a classic statics problem involving a hanging rope.[3] Mathematically, the catenary curve is the graph of the hyperbolic cosine function. The surface of revolution of the catenary curve, the catenoid, is a minimal surface, specifically a minimal surface of revolution. A hanging chain will assume a shape of least potential energy which is a catenary.[4] The mathematical properties of the catenary curve were first studied by Robert Hooke in the 1670s, and its equation was derived by Leibniz, Huygens and Johann Bernoulli in 1691. #ramasonisir #bscmath