Lyapunov Exponents and Stochastic Stability of Quasi-Integrable-Hamiltonian Systems

[+] Author and Article Information
W. Q. Zhu, Z. L. Huang

Department of Mechanics, Zhejiang University, Hangzhou 310027, P.R. China

J. Appl. Mech 66(1), 211-217 (Mar 01, 1999) (7 pages) doi:10.1115/1.2789148 History: Received August 04, 1997; Revised July 08, 1998; Online October 25, 2007


The averaged equations of integrable and nonresonant Hamiltonian systems of multi-degree-of-freedom subject to light damping and real noise excitations of small intensities are first derived. Then, the expression for the largest Lyapunov exponent of the square root of the Hamiltonian is formulated by generalizing the well-known procedure due to Khasminskii to the averaged equations, from which the stochastic stability and bifurcation phenomena of the original systems can be determined approximately. Linear and nonlinear stochastic systems of two degrees-of-freedom are investigated to illustrate the application of the proposed combination approach of the stochastic averaging method for quasi-integrable Hamiltonian systems and Khasminskii’s procedure.

Copyright © 1999 by The American Society of Mechanical Engineers
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