Abstract
In ski racing, the objective is to minimize the time of descent through a prescribed course delineated by poles, or gates, around which the skier must turn. Segments of the course consist of direct paths from one gate to the next, which are usually placed in a regular array at some distance down and across the slope from each other. Finding the path of quickest descent between such pairs of gates is not done simply by following a straight line between them. This problem, known as the brachistochrone problem, requires finding the stationary value of the integral of a function for different paths between two fixed points. It is treated by the calculus of variations and is discussed in any of a number of texts on mathematical physics or mechanics [1].
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References
For example, see J. Mathews and R. L. Walker, Mathematical Methods of Physics (W. A. Benjamin, New York, 1964), p. 307. The discussion here of the brachistochrone problem in the context of skiing is generally indebted to G. Twardokens, Universal Ski Techniques (Surprisingly Well, Reno, NV, 1992), pp. 256–257.
The details of the mathematical development sketched here may be found in G. Reinisch, “A Physical Theory of Alpine Ski Racing,” Spektrum Sportwissenschaft I, 27 (1991).
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© 2004 Springer Science+Business Media New York
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Lind, D.A., Sanders, S.P. (2004). The Brachistochrone Problem: The Path of Quickest Descent. In: The Physics of Skiing. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4345-6_19
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DOI: https://doi.org/10.1007/978-1-4757-4345-6_19
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