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