MATEC Web of Conferences (Jan 2018)

Dynamical behaviour of a compound elastic pendulum

  • Nikolov Svetoslav,
  • Zaharieva Daniela

DOI
https://doi.org/10.1051/matecconf/201814501003
Journal volume & issue
Vol. 145
p. 01003

Abstract

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The aim of the paper is a comprehensive study of the compound elastic pendulum (CEP) with two degrees of freedom to point out the main complex (chaotic) dynamics that it can exhibit. The simplest way to find complex behavior in a nonintegrable Hamiltonian system is firstly to look for homoclinic (heteroclinic) orbit(s). Here, under suitable assumptions, we detect the existence of a homoclinic orbit of CEP and present the equation for it. Moreover, we show that for any value of the small parameter the system has a hyperbolic periodic orbit, whose invariant manifolds intersect themselves transversally.