Received: 5 September 2017 DOI: 10.1002/mma.4650 SPECIAL ISSUE PAPER Dynamical properties of a nonautonomous double pendulum model Marek Lampart 1,2 Jaroslav Zapomˇ el 3 1 IT4Innovations, VŠB - Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava, Czech Republic 2 Department of Applied Mathematics, VŠB - Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava, Czech Republic 3 Department of Dynamics and Vibrations, Institute of Thermomechanics of the CAS, v.v.i., Dolejškova 1402/5, 182 00 Prague 8, Czech Republic Correspondence Marek Lampart, Department of Applied Mathematics, VŠB - Technical University of Ostrava, Tr. 17 listopadu 15, CZ 708 33 Ostrava-Poruba, Czech Republic; or IT4Innovations, VŠB - Technical University of Ostrava, Tr. 17 listopadu 15, CZ 708 33 Ostrava-Poruba, Czech Republic. Email: marek.lampart@vsb.cz Communicated by: J. Vigo-Aguiar Funding information The Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPU II) ; The Ministry of Education, Youth and Sports from the Large Infrastructures for Research, Experimental Development and Innovations, Grant/Award Number: SP2017/122 ; Czech Science Foundation, Grant/Award Number: 15-06621S and P103/15/06700S MOS Classification: 34H20; 34H10; 37N30 This research was motivated by a real technological problem of vibrations of bod- ies hanging on chains or ropes in tubes or spaces limited by walls or other bodies. The studied system has two degrees of freedom. It is formed by two pendulums moving between two walls. Its movement is governed by a set of nonlinear ordi- nary differential equations. The results of the simulations shown that the system exhibits regular and chaotic movement. The simulations were performed for 3 excitation amplitudes and the range of the excitation frequencies between 1 and 30 rad s -1 . The subject of the investigations was the determination of the char- acter of the pendulums' motions and identification of their collisions with the sided walls. KEYWORDS bifurcation, chaos tests, mechanical model, vibration 1 INTRODUCTION A pendulum is a mechanical device that is used for numerous technological or scientific studies and is a substance of many devices having practical application. The nonlinear characteristic of pendulum systems attract a lot of attention being used to describe different phenomena related to oscillations, bifurcation, and chaos. Singh at al 1 investigated a dou- ble pendulum with a stopper at the lower joint. The aim of the study was to inspect the system response and to evaluate Math Meth Appl Sci. 2017;1–9. wileyonlinelibrary.com/journal/mma Copyright © 2017 John Wiley & Sons, Ltd. 1