Huygens and Bernoulli's brachistochrone - Rijksuniversiteit Groningen

More documents

Recommendations

Info

H&B – p.20/27DiscretisationHorizontal layers 1, 2,... ,N of equal width <strong>and</strong> withconstant speed of propagation v j , 1 ≤ j ≤ NLightray follows broken straight line,refraction according to Snell’s lawLimit N → ∞ give cycloid: rolling angle ϕ is doublethe inclination angle with the vertical directionThis assertion needs proof!
H&B – p.21/27Fermat implies Snell (Leibniz 1684)Willebrord Snellius Gottfried Wilhelm Leibniz1580–1626 1646–1716
Page 1 and 2: H&B - p.1/27Huygens and Bernoulli
Page 3 and 4: H&B - p.3/27Huygens and BernoulliCh
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 22 and 23: H&B - p.22/27OpticsPn 1 = 1/v 1α 1
Page 24 and 25: H&B - p.24/27Deduction cycloidSnell
Page 26 and 27: H&B - p.26/27Commentary1. Challenge

Huygens and Bernoulli's brachistochrone - Rijksuniversiteit Groningen

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

Delete template?

Save as template?