Nonlinear Normal Modes in the pendulum system under magnetic excitation

Abstract

Dynamics of two coupled pendulums under magnetic excitation is considered. Inertial components of the pendulums are essentially different, and a ratio of masses is chosen as a small parameter. Padé approximants is used to for the magnetic forces approximation. The small parameter method and the method of multiple scales are used to construct nonlinear normal modes (NNMs), one of them is localized one. Influence of the initial values and the system parameters, including the pendulum masses, change to the NNMs is studied.