Lagrangian Descriptors (LDs) are scalar quantities able to reveal separatrices, manifolds of hyperbolic saddles, and chaotic seas dynamical systems. A popular version the LDs consists in computing arc-length trajectories over a calibrated time-window. Herein we introduce exploit an intrinsic geometrical parametrisation LDs, free time variable, for 1 degree-of-freedom Hamiltonian The depends sol...

multi frequency vibrations of a system of two isotropic circular plates interconnected by a rolling visco-elastic layer that has nonlinear characteristics are considered. the system with two circular plates and interconnecting discrete continually distributed rolling visco nonlinear elastic rheological elements presents the model of hybrid nonlinear system. the analytical solutions of first asy...

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 ...

Philosophers like Duhem and Cartwright have argued that there is a tension between laws' abilities to explain and to represent. Abstract laws exemplify the first quality, phenomenological laws the second. This view has both metaphysical and methodological aspects: the world is too complex to be represented by simple theories; supplementing simple theories to make them represent reality blocks t...