Boundary of the Basin of Attraction for Weakly Damped Primary Resonance

[+] Author and Article Information
R. Haberman, E. K. Ho

Department of Mathematics, Southern Methodist University, Dallas, TX 75275-0156

J. Appl. Mech 62(4), 941-946 (Dec 01, 1995) (6 pages) doi:10.1115/1.2896026 History: Received October 10, 1993; Revised August 23, 1994; Online October 30, 2007


The dissipatively perturbed Hamiltonian system corresponding to primary resonance is analyzed in the case in which two competing stable periodic responses exist. The method of averaging fails as the trajectory approaches the unperturbed homoclinic orbit (separatrix). By using the small dissipation of the Hamiltonian (the Melnikov integral) near the homoclinic orbit, the boundaries of the basin of attraction are determined analytically in an asymptotically accurate way. The selection of the two competing periodic responses is influenced by small changes in the initial conditions. The analytic formula is shown to agree well with numerical computations.

Copyright © 1995 by The American Society of Mechanical Engineers
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