Fractional Calculus - Gauge-institute.org

Gauge Institute Journal, Volume 5, No 1, February 2009H. Vic Dannony( α) = (1− cos2 α),a2Proof:By 5.6,Substitutingwe have,xη=ya= ∫ −1dη.ηη=0η = a sin 2 θ,2y asinα= ,aη− 1 cos1 = θ12sin θ− = sin θ,dη = 2asinθcosθdθ,θ=α2x = 2a ∫ cos θdθθ=0θ=α∫= a (1 + cos 2 θ)dθ2θ=0=a(2α + sin 2 α).2y = asinα= (1 − cos 2 α).a2The Tautochrone problem is treated by Nahin [Nahin] bytraditional methods.20