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A qualitative analysis of the brachistochrone problem with dry friction and maximizing the horizontal range

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Moscow University Mechanics Bulletin Aims and scope

Abstract

The problem of maximizing the horizontal coordinate of a point moving in a vertical plane under the action of gravity and dry friction and the corresponding brachistochrone problem are considered. The optimal control problem is reduced to a boundary value problem for a system of two nonlinear differential equations. A qualitative analysis of the trajectories of this system is carried out, their typical features are found and illustrated by numerical solving of the boundary value problem. It is shown that the normal component of the support reaction should be positive when moving along the optimal curve. The optimality of the found extremals is discussed.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119899, Russia

    A. V. Zarodnyuk & O. Yu. Cherkasov

Authors
  1. A. V. Zarodnyuk
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  2. O. Yu. Cherkasov
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Correspondence to A. V. Zarodnyuk.

Additional information

Original Russian Text © A.V. Zarodnyuk, O.Yu. Cherkasov, 2016, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2016, Vol. 71, No. 4, pp. 54–59.

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Zarodnyuk, A.V., Cherkasov, O.Y. A qualitative analysis of the brachistochrone problem with dry friction and maximizing the horizontal range. Moscow Univ. Mech. Bull. 71, 93–97 (2016). https://doi.org/10.3103/S002713301604004X

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  • DOI: https://doi.org/10.3103/S002713301604004X

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