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Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2024, Volume 11, Issue 2, Pages 371–384
DOI: https://doi.org/10.21638/spbu01.2024.110
(Mi vspua303)
 

MECHANICS

Dynamics of a double pendulum with viscous friction in the joints. I. Mathematical model of motion and construction of the regime diagram

A. S. Smirnovab, I. A. Kravchinskiybc

a Peter the Great St. Petersburg Polytechnic University
b Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg
c CMT-Engineering, 28/2, Bolshoy Sampsonievsky pr., St. Petersburg, 195277, Russian Federation
Abstract: The paper discusses the dynamic behavior of a double mathematical pendulum with identical parameters of links and end loads, which is under the influence of viscous friction in both of its joints with generally different dissipative coefficients. A linear mathematical model of the system motion for small deviations is given, and a characteristic equation containing two dimensionless dissipative parameters is derived. For the case of low damping, approximate analytical expressions are found that make it possible to evaluate and compare with each other the damping factors during the motion of the system on each of the oscillation modes. A diagram of dissipative motion regimes is constructed, which arises when the plane of dimensionless parameters is divided by discriminant curves into regions with a qualitatively different character of the system motion. It is noted that a dissipative internal resonance can take place in the system under consideration, and the conditions for its existence in an analytical form are established, as well as their graphic illustration is also given. This article is the first part of the study of the dynamics of a dissipative double pendulum, the continuation of which will be presented as a separate work “Dynamics of a double pendulum with viscous friction in the joints. II. Dissipative oscillation modes and optimization of damping parameters”.
Keywords: double pendulum, viscous damping, low friction, damping factor, discriminant curve, dissipative regime diagram, dissipative internal resonance.
Received: 07.09.2023
Revised: 28.10.2023
Accepted: 09.11.2023
Document Type: Article
UDC: 517.1
MSC: 47H10, 54H25
Language: Russian
Citation: A. S. Smirnov, I. A. Kravchinskiy, “Dynamics of a double pendulum with viscous friction in the joints. I. Mathematical model of motion and construction of the regime diagram”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 11:2 (2024), 371–384
Citation in format AMSBIB
\Bibitem{SmiKra24}
\by A.~S.~Smirnov, I.~A.~Kravchinskiy
\paper Dynamics of a double pendulum with viscous friction in the joints. I. Mathematical model of motion and construction of the regime diagram
\jour Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
\yr 2024
\vol 11
\issue 2
\pages 371--384
\mathnet{http://mi.mathnet.ru/vspua303}
\crossref{https://doi.org/10.21638/spbu01.2024.110}
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