IJPAM: Volume 82, No. 3 (2013)
THE BRACHISTOCHRONE CURVE:
THE PROBLEM OF QUICKEST DESCENT
THE PROBLEM OF QUICKEST DESCENT
Yutaka Nishiyama
Department of Business Information
Faculty of Information Management
Osaka University of Economics
2, Osumi Higashiyodogawa Osaka, 533-8533, JAPAN
Department of Business Information
Faculty of Information Management
Osaka University of Economics
2, Osumi Higashiyodogawa Osaka, 533-8533, JAPAN
Abstract. This article presents the problem of quickest descent, or the Brachistochrone curve, that may be solved by the calculus of variations and the Euler-Lagrange equation. The cycloid is the quickest curve and also has the property of isochronism by which Huygens improved on Galileo's pendulum.
Received: September 25, 2012
AMS Subject Classification: 34A02, 00A09, 97A20
Key Words and Phrases: brachistochrone curve, law of energy conservation, calculus of variations, Euler-Lagrange equation, cycloid, isochronism, Huygens's pendulum
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 82
Issue: 3
