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Chaos occurs widely in both natural and man-made systems. Recently, examples of the potential usefulness of chaotic behavior have caused growing interest among engineers and applied scientists. In this book the new mathematical ideas in nonlinear dynamics are described in such a way that engineers can apply them to real physical systems. From a review of the first edition by Prof. El Naschie, University of Cambridge: "Small is beautiful and not only that, it is comprehensive as well. These are the spontaneous thoughts which came to my mind after browsing in this latest book by Prof. Thomas Kapitaniak, probably one of the most outstanding scientists working on engineering applications of Nonlinear Dynamics and Chaos today. A more careful reading reinforced this first impression....The presentation is lucid and user friendly with theory, examples, and exercises.... I thought that one can no longer write text books in nonlinear dynamics which could have important impact of fill a gap. Tomasz Kapitaniak's newest book has proved me wrong twofold.".

517.987 --- Systems engineering --- Chaotic behavior in systems --- Control theory --- Nonlinear theories --- Nonlinear problems --- Nonlinearity (Mathematics) --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Engineering systems --- System engineering --- 517.987 Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Design and construction --- Calculus --- Mathematical analysis --- Mathematical physics --- Dynamics --- Machine theory --- Differentiable dynamical systems --- System theory --- Engineering --- Industrial engineering --- System analysis --- Applied mathematics. --- Engineering mathematics. --- Computational intelligence. --- Computational complexity. --- Physics. --- Mathematical and Computational Engineering. --- Computational Intelligence. --- Complexity. --- Mathematical Methods in Physics. --- Numerical and Computational Physics, Simulation. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Complexity, Computational --- Electronic data processing --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Engineering analysis --- Mathematics

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Mathematical physics

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This book presents a three-dimensional model of the complete unicycle–unicyclist system. A unicycle with a unicyclist on it represents a very complex system. It combines Mechanics, Biomechanics and Control Theory into the system, and is impressive in both its simplicity and improbability. Even more amazing is the fact that most unicyclists don’t know that what they’re doing is, according to science, impossible – just like bumblebees theoretically shouldn’t be able to fly. This book is devoted to the problem of modeling and controlling a 3D dynamical system consisting of a single-wheeled vehicle, namely a unicycle and the cyclist (unicyclist) riding it. The equations of motion are derived with the aid of the rarely used Boltzmann–Hamel Equations in Matrix Form, which are based on quasi-velocities. The Matrix Form allows Hamel coefficients to be automatically generated, and eliminates all the difficulties associated with determining these quantities. The equations of motion are solved by means of Wolfram Mathematica. To more faithfully represent the unicyclist as part of the model, the model is extended according to the main principles of biomechanics. The impact of the pneumatic tire is investigated using the Pacejka Magic Formula model including experimental determination of the stiffness coefficient. The aim of control is to maintain the unicycle–unicyclist system in an unstable equilibrium around a given angular position. The control system, based on LQ Regulator, is applied in Wolfram Mathematica. Lastly, experimental validation, 3D motion capture using software OptiTrack – Motive:Body and high-speed cameras are employed to test the model’s legitimacy. The description of the unicycle–unicyclist system dynamical model, simulation results, and experimental validation are all presented in detail.

Engineering. --- Vibration. --- Dynamical systems. --- Dynamics. --- Vibration, Dynamical Systems, Control. --- Classical Mechanics. --- Statistical Physics and Dynamical Systems. --- Biomechanics. --- Dynamics --- Unicycles --- Statistical methods. --- Mechanics. --- Statistical physics. --- Biological mechanics --- Mechanical properties of biological structures --- Biophysics --- Mechanics --- Contractility (Biology) --- Physics --- Mathematical statistics --- Classical mechanics --- Newtonian mechanics --- Quantum theory --- Cycles --- Sound --- Statistical methods --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Statics

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