Dynamical directivity and chaos in some systems with supplementary degrees of freedom

In systems with supplementary degrees of freedom dynamical directivity followed by chaos may exist. Deterministic systems of such types are analyzed in the paper. Their steady state regimes which take place according to dynamically self setting trajectories or vibration modes depending on the eigenfrequencies of the system itself and on the excitation frequencies and parameters are determined. The research is performed by applying approximate analytical methods and numerical ones