2010/01/13 by Rodney Coleman, Coleman, Rodney
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Experimental and Theoretical Physics Studies #FOS: Mathematics #Optimization and Control (math.OC) #Sports Dynamics and Biomechanics #math.OC
paper · pdf · doi:10.48550/arxiv.1001.2181
openalex publication_date 2010/01/13 · arxiv created 2012/11/13 · arxiv updated 2012/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.