INTEGRABILITY IN A NONLINEAR MODEL OF SWING OSCILLATORY MOTION

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.

Automated summary

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.