STOCHASTIC AVERAGING OF QUASI-HAMILTONIAN SYSTEMS

A stochastic averaging method is proposed for quasi-Hamiltonian system s (Hamiltonian systems with light dampings subject to weakly stochasti c excitations). Various versions of the method, depending on whether t he associated Hamiltonian systems are integrable or nonintegrable, res onant or nonresonant, are discussed. It is pointed out that the standa rd stochastic averaging method and the stochastic averaging method of energy envelope are special cases of the stochastic averaging method o f quasi-Hamiltonian systems and that the results obtained by this meth od for several examples prove its effectiveness.