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In this paper, an analytical solution for the problem of finding profiles of gravity flow discharge chutes required to achieve maximum exit velocity under Coulomb friction is obtained by application of variational calculus. The model of a particle which moves down a rough curve in a uniform gravitational field is used to obtain a solution of the problem for various boundary conditions. The projection...
This paper formulates and solves in closed form (expressed by elementary functions) the brachistochrone problem with Coulomb friction of a particle which moves down a rough curve in a uniform gravitational field assuming that the initial velocity of the particle is different from zero. The problem is solved by the application of variational calculus. Two variants are considered: first, the initial...
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