A Generalization of the Classical Brachistochrone Curve A Preliminary Study

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概要

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• The classical Brachistochrone curve is one of fastest descent on a vertical plane. In this paper curves on fastest descent on surfaces that can be represented by elliptic integrals are studied. In the first part it is shown that such curves have to lie on spheres or cones. In the second part curves on cones are studied in detail and it is found that these curves approach to cycloids as cones become cylinders gradually.

• 2010-03-16

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