Planar Brachistochrone of a Particle Attracted in Vacuo by an Infinite Rod - NZJM

摘要

The authors analyze the planar brachistochrone in vacuo under the attraction of an infinite rod, adding a new closed form treatment to the known solutions' collection. Accordingly, a nonlinear boundary value problem: is met, where are fixed and A and k depend on and on the initial speed. The solution's existence and uniqueness are proved noticing that the variational integrand meets the conditions of a Cesari's theorem. This problem, proposed by G. T. Tee in [21] and treated numerically, is solved here in closed form. The trajectory's parametric equations are obtained by means of a generalized, 2-variables, hypergeometric Lauricella confluent function, for the first time used in optimization.