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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H&B – p.8/27Arclength cycloidarclength x = x(ϕ) (using Pythagoras):dx = √ dξ 2 + dη 2 == √ (dξ/dϕ) 2 + (dη/dϕ) 2 dϕ == ̺√2 √ 1 + cos ϕ dϕ = 2̺ cos ϕ 2 dϕ x(ϕ) = 4̺ sin ϕ 2