By Jan Awrejcewicz (eds.)

The publication is a set of contributions dedicated to analytical, numerical and experimental innovations of dynamical structures, awarded on the foreign convention on Dynamical structures: idea and purposes, held in Łódź, Poland on December 2-5, 2013. The reports provide deep perception into either the speculation and purposes of non-linear dynamical platforms, emphasizing instructions for destiny examine. subject matters coated contain: restricted movement of mechanical platforms and monitoring keep an eye on; diversities within the inverse dynamics; singularly perturbed ODEs with periodic coefficients; asymptotic suggestions to the matter of vortex constitution round a cylinder; research of the commonplace and chaotic dynamics; infrequent phenomena and chaos in energy converters; non-holonomic constraints in wheeled robots; unique bifurcations in non-smooth platforms; micro-chaos; power trade of coupled oscillators; HIV dynamics; homogenous adjustments with purposes to off-shore narrow buildings; novel ways to a qualitative research of a dissipative process; chaos of postural sway in people; oscillators with fractional derivatives; controlling chaos through bifurcation diagrams; theories in relation to optical choppers with rotating wheels; dynamics in professional platforms; taking pictures tools for non-standard boundary price difficulties; computerized sleep scoring ruled by means of hold up differential equations; isochronous oscillations; the aerodynamics pendulum and its restrict cycles; restricted N-body difficulties; nano-fractal oscillators and dynamically-coupled dry friction.

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**Extra resources for Applied Non-Linear Dynamical Systems, 1st Edition**

**Example text**

D. Thesis, Kazan (1981) (in Russian) 8. : Nonlinear equations in theory of shells and their linearizations in problems of stability. In: Proceedings of VI Russian Federation Conference on Theory of Plates and Shells, pp. 355–368. Nauka, Moscow (1969) (in Russian) 9. : Solution of the equations of thermoelasticity. In: Proceedings of 3rd National Congress of Applied Mechanics ASME, pp. 685–690, 1958 10. : On the solution of non-linear stability problems of deformable systems. PMM 27(2), 265–274 (1963) (in Russian) 11.

2) or through the periodic shear load action in the shell volume unit (Sect. 3), flexible multilayer rectangular (Sect. 4) and cylindrical shells with gaps (Sect. 5), as well as a flexible plate of infinite length (Sect. 6). J. V. A. Yu. A. V. V. M. Zakharov • V. ru © Springer International Publishing Switzerland 2014 J. 1007/978-3-319-08266-0__5 49 50 J. Awrejcewicz et al. 1 Introduction This chapter addresses an important problem of turbulent wave dynamics exhibited by a solid which has not been satisfactorily explained and clarified yet through the investigations of vibrations of flexible plates and shells.

Regarding the movement pattern of WLLS, current literature (see [3, 7, 8]) often takes the basic idea from the movement of biological worms. However, the mathematical description of these patterns is based on a purely kinematic view, at times just using two states for the system’s actuating elements—elongated and contracted. The generation of specific gaits is discussed, but they are not analyzed and compared in terms of dynamics. Such analyses are the focus of this work. C. Behn ( ) • S. de © Springer International Publishing Switzerland 2014 J.