Abstract
Ann-degree-of-freedom quasi-non-integrable-Hamiltonian system is first reduced to anItôequation of one-dimensional averaged Hamiltonian by using the stochastic averaging method developed by the first author and his coworkers. The necessary and sufficient conditions for the asymptotic stability in probability of the trivial solution of the quasi-non-integrable-Hamiltonian system are then obtained approximately by examining the sample behaviors of the one-dimensional diffusion process of the square-root of averaged Hamiltonian at the two boundaries. A system of linearly and non-linearly coupled two non-linearly damped oscillators subject to parametric excitations of Gaussian white noises is employed as an example to illustrate the procedure, and the effects of non-linear damping and non-linear coupling on the stability are analyzed in detail.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
