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Oscillations of Double Mathematical Pendulum with Internal Friction

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Advances in Mechanical Engineering (MMESE 2022)

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Abstract

This paper investigates the oscillations of a double mathematical pendulum with identical parameters of links and end loads under the action of internal friction in both of its rod elements. Dissipative function of internal friction is constructed, which is a quadratic function with respect to the change rates of forces in the double pendulum rods. Mathematical model of small oscillations of the system is obtained, in which dissipative effects have the third order of smallness. An approximate solution of the problem is based on single-frequency and two-frequency averaging methods. This solution makes possible to analyze the fading of system motions under the action of internal friction for both of each oscillation modes separately under the appropriate initial conditions and in the general case with their simultaneous presence in the solution. The obtained results are presented in the form of visual graphic illustrations, and they may be of certain theoretical and practical interest.

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Authors and Affiliations

  1. Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia

    Alexey S. Smirnov & Boris A. Smolnikov

  2. Institute of Problems of Mechanical Engineering of the Russian Academy of Sciences, St. Petersburg, Russia

    Alexey S. Smirnov & Boris A. Smolnikov

Authors
  1. Alexey S. Smirnov
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  2. Boris A. Smolnikov
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Correspondence to Alexey S. Smirnov .

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Editors and Affiliations

  1. Peter the Great Saint Petersburg Polytechnic University, Saint Petersburg, Russia

    Alexander N. Evgrafov

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Smirnov, A.S., Smolnikov, B.A. (2023). Oscillations of Double Mathematical Pendulum with Internal Friction. In: Evgrafov, A.N. (eds) Advances in Mechanical Engineering. MMESE 2022. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-30027-1_17

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  • DOI: https://doi.org/10.1007/978-3-031-30027-1_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-30026-4

  • Online ISBN: 978-3-031-30027-1

  • eBook Packages: EngineeringEngineering (R0)

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