Summary
The system of two elastically coupled pendulums in a magnetic field is considered when the inertial characteristics of the pendulums differ significantly. In this case, both coupled and localized nonlinear normal modes (NNMs) can be observed. Such modes are constructed by the multiple scales method. The stability of NNMs is studied using a numerical-analytical procedure, which is related to the Lyapunov stability criterion. This stability is assessed by estimating orthogonal variations from the trajectories in the system configuration space. Regions of stability/instability of such modes in the system parameter space are obtained. Numerical simulation includes the construction of trajectories of NNMs in phase and configuration spaces and frequency spectrum, which allows us to detect regular or complex behavior of the system, both for small and significant initial deviations of the pendulums.
