Non-stationary resonance dynamics of weakly coupled pendula

¹ Institute of Chemical Physics, Russian Academy of Science - Kosygin str. 4, Moscow, Russia
² Department of Structural and Geotechnical Engineering, Sapienza University of Rome Via Gramsci 53, Rome, Italy

Received: 11 August 2015
Accepted: 2 November 2015

Abstract

In this letter we fill the gap in understanding the non-stationary Hamiltonian dynamics of the weakly coupled pendula model having significant applications in numerous fields of physics. While common knowledge of this model is predominantly based on the stationary theory and quasi-linear approach to non-stationary dynamics, we consider a strongly nonlinear system without any polynomial approximation of the anharmonic potential. In the adopted asymptotics only closeness to any inter-pendulum resonance frequency is assumed. Being able to explore the whole diapason of initial conditions, two key nonlinear features are revealed by means of the Limiting Phase Trajectories concept: the conditions of intense energy exchange between the pendula and transition to energy localization. The roots and the domain of chaotic behavior are clarified as they are associated with the latter, purely non-stationary, topological transition.