Bernoulli's lightray solution for the brachistochrone problem from ...

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Commentary- Challenge in Acta Eruditorum (1697)Many contemporaries published <strong>solution</strong>sNewton’s was anonymous, however,ex ungue leonem cognavi- Isochrony and tautochrony cycloid dynamicsby harmonic oscillationsJ.L. Lagrange, Mécanique Analytique. 4 ed., 2 vols. Gauthier-Villars et fils, Paris, 1888-89
William Rowan Hamilton- Many contributions to ma<strong>the</strong>matics,physics and astronomy ,principle of least actionW.R. Hamilton, Theory of systems of rays. Trans. Roy. Irish Academy 15 (1828), 69-174—, On a general method in dynamics. Phil. Trans. Roy. Soc. Vol. 124 (1834), 247-308; Secondessay on a general method in dynamics. Phil. Trans. Roy. Soc. Vol. 125 (1835), 95-144
Page 1 and 2: Bernoulli’s lightray solutionfor
Page 3 and 4: IntroductionJohann Bernoulli (1667
Page 5 and 6: Fermat and Snelln 1 sinα = n 2 sin
Page 7 and 8: Bernoulli and Snell- Snell’s law:
Page 9 and 10: A few high school computationsLemma
Page 11: Christiaan Huygens (1629-1695)Chris
Page 15 and 16: Calculus of variations- If q = (x,y
Page 17 and 18: Laws, properties- Energy conservati
Page 19 and 20: Gravitational refraction indexBack
Page 21 and 22: Reconstruction ITime parametrizatio
Page 23 and 24: Scholium I- Reminds of how Newton
Page 25 and 26: Scholium II: lightrays geodesicsGeo
Page 27 and 28: Arclength cycloidarclengths = s(ϕ)

Bernoulli's lightray solution for the brachistochrone problem from ...

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