Научен доклад ID 1352 : 2016/3

Svetoslav Nikolov, Daniela Zaharieva

The simplest way to find complex (chaotic) behavior in a Hamiltonian system, e.g. as a starting point for consideration, is to look for homoclinic (heteroclinic) orbit(s).
In this paper, under suitable assumptions, we detect the existence of a homoclinic orbit of a nonintegrable Hamiltonian system with two degrees of freedom – a compound elastic pendulum and present the equation for it.

open/download as PDF
elastic pendulum homoclinic orbit nonintegrable Hamiltonian systemеластично махало хомоклинична орбита неинтегруема хамилтонава системаSvetoslav Nikolov Daniela ZaharievaBibliography

[1] Brin, M., Stuck, G., Introduction to dynamical systems, Cambridge University Press, Cambridge, 2003.

[2] Nikolov, S., Genov, Ju., Nachev, N., Stability of nonlinear mechanical system with two degrees of freedom, Mechanics, Transport, Communications, vol. 8(1), art. No 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] Vilasi, G., Hamiltonian dynamics, World Scientific, Singapore, 2001.

[5] Lowenstein, J., Essentials of Hamiltonian dynamics, Cambridge University Press, NY, 2012.

[6] Hansmann, H., Local and semi-local bifurcations in Hamiltonian dynamical systems, Springer, Berlin, 2007.

[7] Arnold, V., Mathematical methods of classical mechanics, Springer-Verlag, Heidelberg, 1978.

[8] Wiggins, S., Global bifurcations and chaos. Analytical methods. Springer-Verlag, NY, 1988.

[9] Nikolov, S., Complex behavior of double inverted pendulum with a vertically oscillating suspension point, Mechanics, Transport, Communications, vol. 10(1), art No 0507, 2012.

[10] Brack, M., Tanaka, K., Transcritical bifurcations in nonintegrable Hamiltonian systems, Physical Review E, vol. 77. art. No 046205, 2008.

[11] van der Heijden, G., Yagasaki, K., Horseshoes for the nearly symmetric heavy top, Z. Angew. Math. Phys. (ZAMP), vol. 65, pp. 221-240, 2014.