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

New Zealand Journal of Mathematics

Giovanni Mingari Scarpello¹  Daniele Ritelli¹ 

[1] Dipartimento di matematicaper le scienze economiche e socialiviale Filopanti, 540127 BolognaITALY$$

关键词: ellipsoid;    n dimensions;    surface area;    electrostatic capacity;    Legendre;    elliptic integral.;   

DOI  :  

学科分类：社会科学、人文和艺术（综合）

来源: University of Auckland * Department of Mathematics

【 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.

【 授权许可】

Unknown