Huygens and Bernoulli's brachistochrone - Rijksuniversiteit Groningen
Huygens and Bernoulli's brachistochrone - Rijksuniversiteit Groningen
Huygens and Bernoulli's brachistochrone - Rijksuniversiteit Groningen
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Cycloidal wire profileVertical heightη(ϕ) = 2̺ sin 2 ϕ 2 = 18̺(x(ϕ))2 potential energy “V = mgη” : V (x) = mg8̺ x2−→ equation of motion beadx ′′ = − g 4̺x :a harmonic oscillator with ω = √ g/(4̺)Conclusion: cycloid isochronous curve(also tautochronous ...)H&B – p.9/27