Thermalisation of a coupled pendulum chain

Coupled pendula show complex and unpredictable collective motions and provide a suitable physical model for complex dynamical systems. Starting from the well- known Fermi-Pasta-Ulam experiment coupled oscillators are expected to undergo spontaneous thermalisation, typical of multi-body systems with non-linear interac- tions, and have been studied in order to investigate energy equipartition and second principle of thermodynamics. By means of an automated videotracking appara- tus we have monitored both single and collective motions occurring in a chain of 24 non-linearly coupled pendula on varying the initial conditions (anharmonicity level, number and energy of excited pendula, etc.). Compared to the original FPU model our chain is highly and quickly dissipative and thermalises very early. The energy metric Ω, which is a an indicator of the ergodic entropy, was studied: after an initial transitory phase, it decays as t^(−2) in all different initial configurations we investigated. Moreover, we have observed other noticeable phenomena, e.g. some chaotic behaviour and intrinsic localised modes.