Resonance Bands in a Two Degree of Freedom Hamiltonian System

Authors

J. J. P. Veerman, Portland State UniversityFollow
Philip Holmes, Cornell University

Sponsor

Research supported by NSF grant CME 84-02069.

Published In

Physica D: Nonlinear Phenomena

Document Type

Citation

Publication Date

7-1986

Abstract

In perturbations of integrable two degree of freedom Hamiltonian systems, the invariant (KAM) tori are typically separated by zones of instability or resonance bands inhabited by elliptic and hyperbolic periodic orbits and homoclinic orbits. We indicate how the Melnikov method or the method of averaging can asymptotically predict the widths of these bands in specific cases and we compare these predictions with numerical computations for a pair of linearly coupled simple pendula. We conclude that, even for low order resonances, the first order asymptotic results are generally useful only for very small coupling (ϵ⪅10-4).

Rights

Copyright © 1986 Published by Elsevier B.V.

Description

*At the time of publication, Peter Veerman was affiliated with Cornell University.

Locate the Document

https://doi.org/10.1016/0167-2789(86)90043-6

DOI

10.1016/0167-2789(86)90043-6

Persistent Identifier

https://archives.pdx.edu/ds/psu/36010

Citation Details

Veerman, P., & Holmes, P. (1986). Resonance bands in a two degree of freedom Hamiltonian system. Physica D: Nonlinear Phenomena, 20(2-3), 413-422.