A thin heavy flagpole bent under a transverse wind: his elastica by hypergeometric functions

In this article we are dealing with a uniform cylindrical pole fixed in a vertical direction at its lowest point, and carried to such a height that the vertical position becomes unstable and flexure begins. Simultaneously the wind is assumed to blow so that being active as a transverse load, and the relevant elastica is investigated. The consequent nonlinear differential equation cannot be treated analytically: but its linearized variant, small deflections, can. We have been led to a Airy type equation to be integrated in closed form through the first kind Bessel and the 1F2 generalized hypergeometric functions. The problem has then completely solved: so we make a useful thing for engineering purposes, or better, for testing the relevant numerical algorithms.