Non-integrability of flail triple pendulum

Abstract

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.

22 pages, 13 figures

References in corpus (1)

• On numerical approaches to the analysis of topology of the phase space for dynamical integrability

Cited by in corpus (5)

• Dynamics and non-integrability of the double spring pendulum
• A new model of variable-length coupled pendulums: from hyperchaos to superintegrability
• Dynamics and non-integrability of the variable-length double pendulum: exploring chaos and periodicity via the Lyapunov refined maps
• On numerical approaches to the analysis of topology of the phase space for dynamical integrability
• On the integrability of a system describing the stationary solutions in Bose--Fermi mixtures