Summary
It is shown that the classical Bernoulli's brachistochrone problem and the brachistochrone problem in a central force field may be solved by the maximum principle of Pontryagin. According to the optimum control theory these problems are singular.
Zusammenfassung
In der Arbeit ist gezeigt, daß das klassische Bernoullische brachistochrone Problem und Brachistochronen im zentralen Schwerefeld durch das Pontryagin Maximum Prinzip gelöst werden können. Gemäss Theorie der optimalen Regelung sind diese Probleme singulär.
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References
L. A. Pars,An Introduction to the Calculus of Variations, Heinemann, London, 1962.
M. Athans andP. L. Falb,Optimal Control, McGraw-Hill, New York, 1966.
C. Lanczos,The Variational Principles of Mechanics. University of Toronto Press, 1966.
W. Von Kleinschmidt andH. K. Schulze,Brachistochronen in einem zentralsymmetrischen Schwerefeld, ZAMM50, 234–236, 1970.
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Djukic, D.S., Atanackovic, T.M. A note on the classical brachistochrone. Journal of Applied Mathematics and Physics (ZAMP) 27, 677–681 (1976). https://doi.org/10.1007/BF01591179
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DOI: https://doi.org/10.1007/BF01591179