Solution for a classical problem in the calculus of variations via rationalized Haar functions. (English) Zbl 1265.49023

Summary: A numerical technique for solving the classical brachistochrone problem in the calculus of variations is presented. The brachistochrone problem is first formulated as a nonlinear optimal control problem. Application of this method results in the transformation of differential and integral expressions into some algebraic equations to which Newton-type methods can be applied. The method is general, and yields accurate results.


49K15 Optimality conditions for problems involving ordinary differential equations
65K10 Numerical optimization and variational techniques
70Q05 Control of mechanical systems
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