ARTICLE
An approximate analytical solution of a 4-DOF variable-length pendulum model
1
Lodz University of Technology, Department of Automation, Biomechanics and Mechatronics, Lodz, Poland
Submission date: 2023-11-12
Final revision date: 2024-01-22
Acceptance date: 2024-01-29
Online publication date: 2024-07-09
Publication date: 2024-07-31
Corresponding author
Godiya Yakubu
Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Stefana Żeromskiego 116, 90-924, Łódź, Poland
Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Stefana Żeromskiego 116, 90-924, Łódź, Poland
KEYWORDS
TOPICS
ABSTRACT
In this work, we employ the multiple scale method to introduce a novel analytical solution
for an extended four-degrees-of-freedom dynamical system modeled on a swinging Atwood
machine. We provide a methodology for obtaining the asymptotic solution up to the
second-order approximation for both the swinging and modified swinging Atwood machine,
demonstrating its solvability through the multiple scale approach. Subsequently, we present
a comparative analysis of time histories between numerical and analytical solutions. These
analytical solutions are of particular significance in applied mechanics, given their practical
applications in parametric dynamical models grounded in the pendulum concept
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| eISSN: | 2543-6309 |
| ISSN: | 1429-2955 |
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