English

A detailed analysis of the brachistochrone problem

Optimization and Control 2012-11-14 v2

Abstract

If A and B are two points in the plane, with B lower and to the right of A, then we may consider the trajectory of an object travelling from A to B under the influence of gravity. The search for the trajectory minimising the time taken by the object gives rise to a mathematical optimisation problem involving an indefinite integral. Although the solution of this problem is known, a full detailed handling of the problem does not seem to be available. The aim of this article is to provide such a detailed study.

Keywords

Cite

@article{arxiv.1001.2181,
  title  = {A detailed analysis of the brachistochrone problem},
  author = {Rodney Coleman},
  journal= {arXiv preprint arXiv:1001.2181},
  year   = {2012}
}