Another Look at the Brachistochrone Problem

Details Another Look at the Brachistochrone Problem Another Look at the Brachistochrone Problem

2010-01-13

arxiv.org/abs/1001.2181v1

Mathematics

Optimization and Control

Scientific paper

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.

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