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 recommendations of dynamical platforms, provided on the foreign convention on Dynamical structures: conception and purposes, held in Łódź, Poland on December 2-5, 2013. The reviews supply deep perception into either the speculation and functions of non-linear dynamical structures, emphasizing instructions for destiny examine. themes coated comprise: restricted movement of mechanical structures and monitoring regulate; 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 ordinary and chaotic dynamics; infrequent phenomena and chaos in energy converters; non-holonomic constraints in wheeled robots; unique bifurcations in non-smooth structures; micro-chaos; strength trade of coupled oscillators; HIV dynamics; homogenous variations with functions to off-shore slim constructions; novel methods to a qualitative learn of a dissipative method; chaos of postural sway in people; oscillators with fractional derivatives; controlling chaos through bifurcation diagrams; theories with regards to optical choppers with rotating wheels; dynamics in professional structures; taking pictures equipment for non-standard boundary price difficulties; automated sleep scoring ruled through 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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The theory of wavelets is widely used in identification problems, where a studied system evolution is deduced from the wavelet transform response. Wavelets of the Daubechies, Morlet, and Gauss families are used to detect faults in gears and gearboxes as well as to estimate the location of cracks [21, 25, 30]. The wavelet-type analysis is applied to lumped mechanical systems governed by ordinary differential equations [12, 17]. The proposed procedure can be viewed as a logarithmic transform applied to a fitted component of the original response.

10) whereby these speed thresholds only depend on N and ˛. Remark 2. , mi D m; their actual value is not required to find these speed thresholds for switching the number of active spikes. Now, if the slope is known (measured), it is then possible to choose adequate gaits, with respect to low spike forces. Remark 3. The estimate of the actuator forces (see (8)) gives identical speed thresholds, as it differs from the spike force estimate only by the addition of a weight term of one mass; this term does not influence the intersection of curves in Fig.

Since all system parameters are assumed to be unknown or, more precisely, uncertain, an adaptive controller is used to achieve the tracking of certain gaits. After finding optimal gaits, a procedure for automatic gait shift based on the measurement of certain restricted system variables is implemented. 1 Modeling The starting point is the chain of mass points in a common straight line as shown in Fig. 1. t / (i D 0; : : : ; n) are the current coordinates of the segments. t /. , they restrict velocities from being negative [10].

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