Generalizations of the Brachistochrone Problem

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dc.creatorGemmer, J.
dc.creatorUmble, R.
dc.creatorNolan, M.
dc.date2006-12-15
dc.date2009-01-27
dc.date.accessioned2026-07-07T12:34:37Z
dc.date.available2026-07-07T12:34:37Z
dc.descriptionConsider a frictionless surface S in a gravitational field that need not be uniform. Given two points A and B on S, what curve is traced out by a particle that starts at A and reaches B in the shortest time? This paper considers this problem on simple surfaces such as surfaces of revolution and solves the problem two ways: First, we use conservation of mechanical energy and the Euler-Lagange equation; second, we use geometrical optics and the eikonal equation. We conclude with a discussion of the relativistic effects at relativistic velocities.
dc.description12 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/math-ph/0612052
dc.identifierhttp://arxiv.org/abs/math-ph/0612052
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217499
dc.subjectMathematical Physics
dc.titleGeneralizations of the Brachistochrone Problem
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