Author:
Nikolov Svetoslav,Zaharieva Daniela
Abstract
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.
Reference24 articles.
1. Brin M., Stuck G., Introduction to dynamical systems (CUP, Cambridge, 2003)
2. Nikolov S., Genov Ju., Nachev N., Mechanics, Transport, Commun. 8, 0472 (2010)
3. Shilnikov L., Shilnikov A., Turaev D., Chua L., Methods of qualitative theory in nonlinear dynamics (Part II, World Scientific, Singapore, 2001)
4. Afraimovich V., Gonchenko S., Lerman L., Shilnikov A., Turaev D.., Regular and Chaotic Dynamics 19, 435-460 (2014)