Regular and chaotic motions in Hénon-Heiles like Hamiltonian

Authors

IDUGBA MATHIAS ECHI
ALEXANDER NWABEZE AMAH
EMMANUEL ANTHONY

DOI

10.3906/fiz-1208-5

Abstract

The dynamics of a system subjected to a potential equal to the sum of the Hénon--Heiles potential and that of hydrogen in an electric field was studied. The 4 Hamilton's equations of motion follow from the Hamiltonian and they were integrated numerically using the Runge-Kutta fourth order method. The Poincaré surface of a section fixed at x = 0 and px> 0 was used to reduce the phase space to a 2-dimensional plane. The analysis of the Poincaré surface, the Lyapunov exponent, and the autocorrelation shows that as the constant of motion, E, increases from 0.30 to 0.45, the dynamics makes a transition from periodic and quasi-periodic to chaotic motions.

Keywords

Hamiltonian, Hénon-Heiles, Poincaré section, Lyapunov exponent, autocorrelation

First Page

380

Last Page

386

Recommended Citation

ECHI, IDUGBA MATHIAS; AMAH, ALEXANDER NWABEZE; and ANTHONY, EMMANUEL (2013) "Regular and chaotic motions in Hénon-Heiles like Hamiltonian," Turkish Journal of Physics: Vol. 37: No. 3, Article 14. https://doi.org/10.3906/fiz-1208-5
Available at: https://journals.tubitak.gov.tr/physics/vol37/iss3/14