Regular and complex behaviour in the pendulum system under a magnetic field

Abstract

Dynamics of two coupled pendulums under a magnetic field are considered by taking into account a dissipation in the system. Inertial components of the pendulums are essentially different, and a ratio of masses is chosen as a small parameter. Padé approximants is used for the magnetic forces approximation. The method of multiple scales is used to construct nonlinear normal modes (NNMs), one of them is a localized one. An appearance of the complex behaviour when the system parameters change is investigated.