Huygens and Bernoulli's brachistochrone - Rijksuniversiteit Groningen

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H&B – p.26/27Commentary1. Challenge in Acta Eruditorum (twice)Many contemporaries sent in solutionNewton’s was anonymous, however,ex ungue leonem cognavi2. Nowadays excercise in course in Calculus ofqVariations e.g., with Lagrangian L(h, h ′ 1+(h) =′ ) 2−2ghH.H. Goldstine, A History of the Calculus of Variations from the 17th through the 19th Century.Studies in the History of Mathematics and Physical Sciences 5, Springer-Verlag (1980)
H&B – p.27/27Background bibliography1. J.M. Aarts, Meetkunde: facetten van de planimetrie en stereometrie, Epsilon Uitgaven 47(2000)2. V.I. Arnold, Huygens & Barrow, Newton & Hooke. Birkhäuser (1990)3. O. Bottema, Theoretische Mechanica, Epsilon Uitgaven 3 (1985)4. H.W. Broer, Huygens, Bernoulli en enige atmosferische optica. (2011) (in preparation)5. H. Erlichson, Johann Bernoulli’s brachistochrone solution using Fermat’s principle ofleast time. Eur. J. Phys. 20 (1999) 299–3046. J.A. van Maanen, Een Complexe Grootheid, leven en werk van Johann Bernoulli,1667–1748. Epsilon Uitgaven 34 (1995)
Page 1 and 2: H&B - p.1/27Huygens and Bernoulli
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Page 6 and 7: H&B - p.6/27Commentary1. Potential
Page 8 and 9: H&B - p.8/27Arclength cycloidarclen
Page 10: H&B - p.10/27Evolute and evolventSo
Page 14 and 15: The master himself . . .H&B - p.14/
Page 16 and 17: H&B - p.16/27Detailed formulation1.
Page 18 and 19: H&B - p.18/27Johann Bernoulli’s s
Page 20 and 21: H&B - p.20/27DiscretisationHorizont
Page 22 and 23: H&B - p.22/27OpticsPn 1 = 1/v 1α 1
Page 24 and 25: H&B - p.24/27Deduction cycloidSnell

Huygens and Bernoulli's brachistochrone - Rijksuniversiteit Groningen

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