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American Journal of Physics -- September 1987 -- Volume 55, Issue 9, pp. 844

The rolling unrestrained brachistochrone

Ju‐xing Yang, David G. Stork, and David Galloway

Department of Physics, Clark University, Worcester, Massachusetts 01610

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We have generalized the unrestained brachistochrone problem to include rolling objects in order to construct a demonstration brachistochrone track. Due to the nature of the constraints this well‐posed extremal problem cannot be solved using the techniques of Euler and Lagrange. The solution, parametrized by a measure of the generalized cylinder’s moment of inertia, reduces to that for the (sliding) unrestrained brachistochrone in the limit of vanishing moment of inertia.

KEYWORDS and PACS

Keywords

CLASSICAL MECHANICS, ROLLING, BOUNDARY−VALUE PROBLEMS, EQUATIONS OF MOTION, BENCH−SCALE EXPERIMENTS

PACS

  • 45.05.+x

    General theory of classical mechanics of discrete systems

  • 01.50.My

    Demonstration experiments and apparatus

History
Received Nov 1985
Accepted Sep 1986

PUBLICATION DATA

ISSN

0002-9505 (print)  

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1119/1.15001


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