Synchronization and decoherence in a self-excited inertia-wheel multiple rigid-body dynamical system

We investigate the synchronization and decoherence of a self-excited inertia wheel multiple rigid-body dynamical system. We employ an Euler-Lagrange formulation to derive a nondimensional state space that governs the dynamics of a coupled pendula array where each element incorporates an inertia wheel. The dynamical system exhibits multiple equilibria, periodic limit-cycle oscillations, quasiperiodic, and chaotic oscillations and rotations. We make use of a combined approach including a singular perturbation multiple time scale and numerical bifurcation methodologies to determine the existence of synchronized and decoherent solutions in both weakly and strongly nonlinear regimes, respectively. The analysis reveals that synchronous oscillations are in-phase, whereas quasiperiodic oscillations are anti-phase. Furthermore, the non-stationary rotations are found to exhibit combinations of oscillations and rotations of the individual elements that are asynchronous. A Kuramoto order parameter analysis of representative solutions in various bifurcation regimes reveals the existence of chimera-like solutions where two elements are synchronized, whereas the third is desynchronized. Moreover, synchronous solutions were found to coexist with stable chimera solutions with a constant phase difference between the oscillators.