3.8 Article

INTEGRABILITY IN A NONLINEAR MODEL OF SWING OSCILLATORY MOTION

Journal

JOURNAL OF GEOMETRY AND SYMMETRY IN PHYSICS
Volume 65, Issue -, Pages 93-108

Publisher

BULGARIAN ACAD SCIENCES, INST MECHANICS
DOI: 10.7546/jgsp-65-2023-93-108

Keywords

Integrability; Lagrangian and Hamiltonian equations of motion; non-linear dynamical systems; swing oscillatory motion

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The aim of this paper is to investigate the integrable cases of a compound pendulum system consisting of a rider and a swing. Our analytical calculations reveal that this system has two integrable cases when the dumbbell lengths and point-masses meet certain conditions, and when the gravitational force is neglected.
Nonlinear dynamical systems can be studied in many different directions: i) find-ing integrable cases and their analytical solutions, ii) investigating the algebraic nature of the integrability, iii) topological analysis of integrable systems, and so on. The aim of the present paper is to find integrable cases of a dynamical system describing the rider and the swing pumped (from the seated position) as a com-pound pendulum. As a result of our analytical calculations, we can conclude that this system has two integrable cases when: 1) the dumbbell lengths and point -masses meet a special condition, 2) the gravitational force is neglected.

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