2012/11/26 by Maria Przybylska, Wojciech Szumiński · 17 citations
Engineering · Mathematics · Physics and Astronomy · #Algebra over a field #Control and Dynamics of Mobile Robots #Differential (mechanical device) #Differential Galois theory #Differential equation #Dynamics and Control of Mechanical Systems #Embedding problem #Galois group #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Pendulum #Physics #Pure mathematics #Quantum mechanics #Type (biology) #math-ph #math.DS #math.MP #msc:70F07 #msc:70H07 #msc:70H12 #nlin.CD
paper · pdf · doi:10.1016/j.chaos.2013.04.008
published in Chaos Solitons & Fractals 53, 60-74 (Elsevier BV) · 22 pages, 13 figures
arxiv created 2012/11/26 · openalex publication_date 2013/06/10 · arxiv updated 2013/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider a special type of triple pendulum with two pendula attached to end mass of another one. Although we consider this system in the absence of the gravity, a quick analysis of of Poincaré cross sections shows that it is not integrable. We give an analytic proof of this fact analysing properties the of differential Galois group of variational equation along certain particular solutions of the system.