STOCHASTIC AVERAGING OF QUASI-NONINTEGRABLE-HAMILTONIAN SYSTEMS

A stochastic averaging method is proposed to predict approximately the response of multi-degree-of-freedom quasi-nonintegrable-Hamiltonian s ystems (nonintegrable Hamiltonian systems with lightly linear and (or) nonlinear dampings and subject to weakly external and (or)parametric excitations of Gaussian white noises). According to the present method , a one-dimensional approximate Fokker-Planck-Kolmogorov equation for the transition probability density of the Hamiltonian cart be construc ted and the probability density and statistics of the stationary respo nse of the system can be readily obtained. The method is compared with the equivalent nonlinear system method for stochastically excited and dissipated nonintegrable Hamiltonian systems and extended to a more g eneral class of systems. An example is given to illustrate the applica tion and validity of the present method and the consistency of the pre sent method and the equivalent nonlinear system method.