Bernoulli's lightray solution for the brachistochrone problem from ...
Bernoulli's lightray solution for the brachistochrone problem from ...
Bernoulli's lightray solution for the brachistochrone problem from ...
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Calculus of variations- If q = (x,y) <strong>the</strong>n Euler–Lagrange equationsddτddτ∂L∂ẋ = ∂L∂x∂L∂ẏ = ∂L∂ynecessary & sufficient <strong>for</strong> local optimality ofI- under small variations ofq,while keeping endpointsq(τ 1 ) andq(τ 2 ) fixed- in current optical setting also minimalL. Euler, Leonhardi Euleri Opera Omnia. 72 vols., Bern 1911-1975J.L. Lagrange, Œuvres. A. Serret and G. Darboux eds., Paris 1867-1892
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