Dynamical behaviour of a compound elastic pendulum

Svetoslav Nikolov, Daniela Zaharieva, V.M. Vassilev, S.G. Nikolov, M.D. Datcheva, Y.P. Ivanova
2018 MATEC Web of Conferences  
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
more » ... f the small parameter the system has a hyperbolic periodic orbit, whose invariant manifolds intersect themselves transversally.
doi:10.1051/matecconf/201814501003 fatcat:7hslmmgcffdx7lw5wtzi2tabwe