Abstract
this paper introduces a numerical technique for solving the classic brachistochrone problem. The brachistochrone problem is first formulated as a nonlinear optimal control problem. Using the Legendre-Gauss-Lobatto nodes we construct the Nth degree polynomial approximation of the state and the control variables. Application of this method results in the transformation of differential and integral expressions into some algebraic equation to which Newton type methods can be applied. The method is general, easy to implement and yields very accurate results. Using this method, the solution to the brachistochrone problem is compared with those in the literature.
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