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International Conference on Industrial Engineering

ICIE 2018: Proceedings of the 4th International Conference on Industrial Engineering pp 1071–1078Cite as

On Proof of the Generalized Lagrange Variational Principle

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Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Abstract

The proof of the generalized Lagrange variational principle for the case when the velocity field is a vortex of some auxiliary vector field is given in the present paper. The proof is obtained for Newtonian fluids. It is demonstrated that the generalized Lagrange functional takes a minimum value on a real field. The generalized Lagrange variational principle extends the class of solving problems to quasistationary ones and can be applied to solve problems in the hydrodynamic lubrication theory. To verify the theoretical results, a numerical solution of the variational problem of fluid flow in a thin layer between rigid parallel plates is performed. The numerical results match with the analytical results with a high accuracy.

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Author information

Authors and Affiliations

  1. Orel State University named after I.S. Turgenev, 95, Komsomolskaya St., Orel, 302023, Russia

    A. V. Kornaev

Authors
  1. A. V. Kornaev
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Correspondence to A. V. Kornaev .

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Editors and Affiliations

  1. South Ural State University, Chelyabinsk, Russia

    Andrey A. Radionov

  2. Platov South-Russian State Polytechnic University, Novocherkassk, Russia

    Oleg A. Kravchenko

  3. South Ural State University, Chelyabinsk, Russia

    Victor I. Guzeev

  4. South Ural State University, Chelyabinsk, Russia

    Yurij V. Rozhdestvenskiy

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Kornaev, A.V. (2019). On Proof of the Generalized Lagrange Variational Principle. In: Radionov, A., Kravchenko, O., Guzeev, V., Rozhdestvenskiy, Y. (eds) Proceedings of the 4th International Conference on Industrial Engineering. ICIE 2018. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-95630-5_112

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  • DOI: https://doi.org/10.1007/978-3-319-95630-5_112

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-95629-9

  • Online ISBN: 978-3-319-95630-5

  • eBook Packages: EngineeringEngineering (R0)

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