Abstract or Additional Information
A new approach to non-stationary nonlinear dynamics, based on the concept of Limiting Phase Trajectories (LPTs) is presented. The systems under consideration are finite nonlinear oscillatory chains which can be identified, e.g., as the dynamical models of mechanical structures, polymer macromolecules or carbon nanotubes (CNTs). The LPT describes the most intensive energy exchange between weakly coupled parts of the system which can be considered as effective particles (EPs). They represent the excitations alternative to Nonlinear Normal Modes (NNMs) which are not involved into the processes with the energy exchange and demonstrate the wave-like behavior. It is possible to speak about distinctive wave-particle duality (WPD) in the framework of classical mechanics, and manifestation of particle-like or wave-like behavior depends on the initial conditions or on the type of attractor (it may be NNM as well as LPT).
Due introducing the EPs the physical nature of the WPD becomes apparent (when the particles themselves are strongly coupled, and the NNMs are resonant, that means their coherence, the EPs are weakly coupled). The transition from the most intensive energy exchange to the energy localization in the part of the system is also naturally described in terms of EPs and LPTs.
The presented approach has significant applications connected with elaboration of the energy traps, synchronization of oscillators, providing the energy exchange and localization in CNTs etc., which will be described.