Quasi-periodic and Chaotic Motions in Nonlinear Hamiltonian Systems

Dr. Albert Luo

Department of Mechanical and Industrial Engineering

Southern Illinois University

In this talk, the mechanism of chaotic motion in nonlinear Hamiltonian systems is presented based on the KAM theory and resonance overlap criterion. The internal resonances and the corresponding chaotic motions are determined analytically for weak interactions. A numerical method based on the energy spectrum is introduced for prediction of quasi-periodic and chaotic motions in nonlinear Hamiltonian systems. The presented numerical method can be applied to non-integrable, nonlinear Hamiltonian systems with many degrees of freedom. The mathematical theory should further be developed for a better prediction of chaotic and quasi-periodic motions in nonlinear Hamiltonian systems with many degrees of freedom.