Applied Non-Linear Dynamical Systems by Jan Awrejcewicz (eds.)

By Jan Awrejcewicz (eds.)

The publication is a suite of contributions dedicated to analytical, numerical and experimental concepts of dynamical structures, awarded on the foreign convention on Dynamical structures: idea and purposes, held in Łódź, Poland on December 2-5, 2013. The reviews provide deep perception into either the idea and purposes of non-linear dynamical platforms, emphasizing instructions for destiny examine. subject matters coated contain: limited movement of mechanical platforms and monitoring keep watch over; diversities within the inverse dynamics; singularly perturbed ODEs with periodic coefficients; asymptotic options to the matter of vortex constitution round a cylinder; research of the normal and chaotic dynamics; infrequent phenomena and chaos in strength converters; non-holonomic constraints in wheeled robots; unique bifurcations in non-smooth platforms; micro-chaos; strength alternate of coupled oscillators; HIV dynamics; homogenous differences with purposes to off-shore narrow constructions; novel ways to a qualitative research of a dissipative approach; chaos of postural sway in people; oscillators with fractional derivatives; controlling chaos through bifurcation diagrams; theories in terms of optical choppers with rotating wheels; dynamics in specialist structures; capturing equipment for non-standard boundary price difficulties; automated sleep scoring ruled by way 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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A. Krysko et al. Acknowledgements This work has been supported by the grant RFBR No. 12-01-31204 and the National Science Centre of Poland under the grant MAESTRO 2, No. 2012/04/A/ST8/00738, for the years 2013–2016. References 1. : Stability of Shells Under Non-Symmetric Deformation. Nauka, Moscow (1988) (in Russian) 2. : Thermodynamics of Plates and Shells. Springer, Berlin (2007) 3. : On the memory of nonlinear differential equations in theory of plates. Vestnik Niznegorodskogo Universiteta im.

This happens even before the reference speed is reduced, because the Fig. 4 Left, worm movement; right, reference speed vN ref Gear Shift Patterns in Uncertain Terrestrial Locomotion Systems 47 Fig. 2;N D4 , as seen in (10), so that the gait with a D 2 is considered optimal. The speed is then reduced to a value that requires the gait with a D 3 to be used. Later, when the slope is smaller, the gait is shifted back to a D 2. Within t D Œ0; 10 s the maxima of the spike forces [see Fig. 5(left)] adhere to the reference value very closely.

However, the situation changes qualitatively beginning from N D 13. Namely, the dynamical properties of the cylindrical shell are stabilized and a further increase of N does not improve the obtained results either qualitatively or quantitatively. Therefore, beginning from N D 13, a convergent series is obtained and all further computations are carried out for N D 13. '0 / for N D 13 reported in [15]. '0 / reported by Andreev et al. [1] for the closed cylindrical shell for D 2 are in agreement with the results obtained by our method.

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