Regular and Complex Behavior in the Pendulum System Under a Magnetic Field

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