Phase resonance nonlinear modes of mechanical systems

Nonlinear Normal Modes of Vibrating Mechanical Systems and Their Applications

Relative Nonlinear Normal Modes of Hamiltonian Systems

We generalize theWeinstein-Moser theorem on the existence of nonlinear normal modes (i.e., periodic orbits) near an equilibrium in a Hamiltonian system to a theorem on the existence of relative periodic orbits near a relative equilibrium in a Hamiltonian system with continuous symmetries. More specifically we significantly improve a result proved earlier jointly with Tokieda: we remove a techni...

Comment on "Nonlinear resonance and chaos in the relativistic phase space for driven nonlinear systems"

Kim and Lee @Phys. Rev. E 52, 473 ~1995!# report relativity-induced resonances in periodically driven oscillators. We comment that zero-dispersion nonlinear resonance ~ZDNR! will occur in some of the systems considered, outline the physical origins of the ZDNR, and propose an explanation of a discrepancy noted by Kim and Lee between their theoretical and numerical values of the energy at the st...

Relative normal modes for nonlinear Hamiltonian systems

An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework of a classical result by Weinstein and Moser on the existence of periodic orbits in the energy levels surrounding a stable equilibrium.The estimate obtained i...

Nonlinear Dynamics and Control of Mechanical Systems

The goal of this session is to survey some of the modern trends in nonlinear dynamics and control theory. The unifying theme of this session is the use of intrinsic dynamical properties of mechanical systems in the design of control strategies. In particular, geometric approaches to dynamics, optimization and control are presented. The following topics will be addressed: Hamiltonian systems on ...