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

More documents

Recommendations

Info

Bernoulli’s lightray solutionFermat principle of least time for light rays optical solution in mechanical setting- Discrete approximation in horizontal layerseach layer homogeneous and isotropic refraction index n = 1/v (c = 1)- Fermat principle⇒- inside layer:ray = straight line with velocity v = 1/n- at boundary: Snell’s lawG.W. Leibniz, Nova methodus pro maximis et minimis. Acta Eruditorum 1684. In: D.J. Struik, Asource book in mathematics 1200–1800. Harvard University Press 1969, 271-281
Fermat and Snelln 1 sinα = n 2 sinβProof: Let x = x C indicate position of Ct AC = n 1 |A−C| andt CB = n 2 |C −B|
Page 1 and 2: Bernoulli’s lightray solutionfor
Page 3: IntroductionJohann Bernoulli (1667
Page 7 and 8: Bernoulli and Snell- Snell’s law:
Page 9 and 10: A few high school computationsLemma
Page 11 and 12: Christiaan Huygens (1629-1695)Chris
Page 13 and 14: William Rowan Hamilton- Many contri
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 ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?