An approximate analytical solution of a 4-DOF variable-length pendulum model

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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Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).