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Optimization of Oscillation Damping Modes of a Spatial Double Pendulum: 2. Solution of the Problem and Analysis of the Results

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Abstract

This study is a continuation of the article “Optimization of oscillation damping modes of a spatial double pendulum: 1. Formulation of the problem,” in which the problem of the optimal oscillation damping of a double pendulum with hinged noncollinear axes was formulated. Passive damping (viscous friction) is considered separately, and the possibility of additional account of active impacts (collinear control) is also explored. Two optimization criteria are introduced that characterize the efficiency of the damping of system motion: first, the degree of stability is maximized, and then the integral energy-time criterion is minimized. The optimal values of the parameters of the damping variants under consideration are determined by applying both criteria in finding the exact solution of the problem in a linear model. The results obtained are presented as visual graphic illustrations which enable determination of their main qualitative and quantitative features. The conclusions made can be useful in studying the motions of manipulators and various robotic structures.

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REFERENCES

  1. A. S. Smirnov and B. A. Smolnikov, “Optimization of oscillation damping modes of a spatial double pendulum: 1. Formulation of the problem,” Vestn. St Petersburg Univ.: Math. 55, 243–248 (2022). https://doi.org/10.1134/S1063454122020133

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  4. A. S. Smirnov and B. A. Smol’nikov, “Optimal damping of free oscillations in linear mechanical systems,” Mashinostr. Inzh. Obraz., No. 3(52), 8–15 (2017).

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Authors and Affiliations

  1. Peter the Great St. Petersburg Polytechnic University, 195251, St. Petersburg, Russia

    A. S. Smirnov & B. A. Smolnikov

  2. Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, 199178, St. Petersburg, Russia

    A. S. Smirnov & B. A. Smolnikov

Authors
  1. A. S. Smirnov
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  2. B. A. Smolnikov
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Corresponding authors

Correspondence to A. S. Smirnov or B. A. Smolnikov.

Additional information

Translated by M. Shmatikov

The first part of the study is published in: A. S. Smirnov and B. A. Smolnikov, “Optimization of Oscillation Damping Modes of a Spatial Double Pendulum: 1. Formulation of the Problem.” Vestnik St. Petersburg University Mathematics 55, 243—248 (2022). https://doi.org/10.21638/spbu01.2022.215

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Smirnov, A.S., Smolnikov, B.A. Optimization of Oscillation Damping Modes of a Spatial Double Pendulum: 2. Solution of the Problem and Analysis of the Results. Vestnik St.Petersb. Univ.Math. 56, 93–106 (2023). https://doi.org/10.1134/S1063454123010132

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  • DOI: https://doi.org/10.1134/S1063454123010132

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