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Dynamical Systems Theory and Applications

DSTA 2017: Dynamical Systems in Applications pp 451–460Cite as

Support Reaction in the Brachistochrone Problem in a Resistant Medium

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 249))

Abstract

The horizontal coordinate’s maximization problem as well as related the brachistochrone problem are considered. The particle is moving in the vertical plane under influence of gravity, viscous drag that proportional to n-th degree of the velocity. The reaction of the basement is considered as a control. The optimal control problem is reduced to the boundary value problem for the system of two nonlinear equations. It was established that the reaction force of the basement could change its sign no more than one time, moreover, it changes only from the negative value to the positive value. The qualitative features of the optimal control allows to elaborate the results obtained in other studies.

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Acknowledgements

This work was supported by RFBR according to the research project No 18-01-00538 and No 17-08-01366.

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Authors and Affiliations

  1. Moscow State Iniversity, Leninskie gori 1, Moscow, Russia

    Alena Zarodnyuk & Oleg Cherkasov

Authors
  1. Alena Zarodnyuk
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  2. Oleg Cherkasov
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Correspondence to Oleg Cherkasov .

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Editors and Affiliations

  1. Dept. of Autom., Biomech. and Mechatr., Łódź University of Technology Dept. of Autom., Biomech. and Mechatr., Lodz, Poland

    Jan Awrejcewicz

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Zarodnyuk, A., Cherkasov, O. (2018). Support Reaction in the Brachistochrone Problem in a Resistant Medium. In: Awrejcewicz, J. (eds) Dynamical Systems in Applications. DSTA 2017. Springer Proceedings in Mathematics & Statistics, vol 249. Springer, Cham. https://doi.org/10.1007/978-3-319-96601-4_40

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