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.16/27Detailed formulation1. K(ϕ) is tangent to E <strong>and</strong> perpendicular to C ;2. |K(ϕ)| is radius of curvature of C in C(ϕ)Comments:- Pendulum attached to cusp of Echord evolves along ‘cheeks’ E=⇒ mass follows C- K⊥C ∼ instantaneous rotation in rolling-wheelconstruction of cycloid;NB: K⊥C ⇒ dynamics of friction-less beadH.W. Broer, <strong>Huygens</strong>’ isochrone slinger. Euclides 70(4) (1995) 110-117