First-passage time of quasi-non-integrable-Hamiltonian system

Studies on first-passage failure are extended to the multi-degree-of-freedo m quasi-non-integrable-Hamiltonian systems under parametric excitations of Gaussian white noises in this paper. By the stochastic averaging method of energy envelope, the system's energy can be modeled as a one-dimensional ap proximate diffusion process by which the classical Pontryagin equation with suitable boundary conditions is applicable to analyzing the statistical mo ments of the first-passage time of an arbitrary order. An example is studie d in detail and some numerical results are given to illustrate the above pr ocedure.