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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<strong>Huygens</strong>’s isochronous curveHooke <strong>and</strong> Newton ⇒equation of motion springNotation:mx ′′ = −kxx ′ (t) = dx(t) ,x ′′ (t) = d2 x(t)dt dt 2Abbreviate ω = √ k/m, get solutionx(t) = R cos(ωt + φ)Period P = 2π/ω independent of amplitude R:isochronyH&B – p.4/27
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