Chaotic Oscillations in Mechanical Systems
Author: Tomasz Kapitaniak
Publisher: Manchester University Press
Published: 1991
Total Pages: 240
ISBN-13: 9780719033643
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Applied Nonlinear Dynamics And Chaos Of Mechanical Systems With Discontinuities
Author: Bram De Kraker
Publisher: World Scientific
Published: 2000-04-28
Total Pages: 462
ISBN-13: 9814497908
DOWNLOAD EBOOKRapid developments in nonlinear dynamics and chaos theory have led to publication of many valuable monographs and books. However, most of these texts are devoted to the classical nonlinear dynamics systems, for example the Duffing or van der Pol oscillators, and either neglect or refer only briefly to systems with motion-dependent discontinuities. In engineering practice a good part of problems is discontinuous in nature, due to either deliberate reasons such as the introduction of working clearance, and/or the finite accuracy of the manufacturing processes.The main objective of this volume is to provide a general methodology for describing, solving and analysing discontinuous systems. It is compiled from the dedicated contributions written by experts in the field of applied nonlinear dynamics and chaos.The main focus is on mechanical engineering problems where clearances, piecewise stiffness, intermittent contact, variable friction or other forms of discontinuity occur. Practical applications include vibration absorbers, percussive drilling of hard materials and dynamics of metal cutting.
Introduction To Control Of Oscillations And Chaos
Author: Alexander L Fradkov
Publisher: World Scientific
Published: 1998-10-20
Total Pages: 407
ISBN-13: 9814497665
DOWNLOAD EBOOKThis book gives an exposition of the exciting field of control of oscillatory and chaotic systems, which has numerous potential applications in mechanics, laser and chemical technologies, communications, biology and medicine, economics, ecology, etc.A novelty of the book is its systematic application of modern nonlinear and adaptive control theory to the new class of problems. The proposed control design methods are based on the concepts of Lyapunov functions, Poincare maps, speed-gradient and gradient algorithms. The conditions which ensure such control goals as an excitation or suppression of oscillations, synchronization and transformation from chaotic mode to the periodic one or vice versa, are established. The performance and robustness of control systems under disturbances and uncertainties are evaluated.The described methods and algorithms are illustrated by a number of examples, including classical models of oscillatory and chaotic systems: coupled pendula, brusselator, Lorenz, Van der Pol, Duffing, Henon and Chua systems. Practical examples from different fields of science and technology such as communications, growth of thin films, synchronization of chaotic generators based on tunnel diods, stabilization of swings in power systems, increasing predictability of business-cycles are also presented.The book includes many results on nonlinear and adaptive control published previously in Russian and therefore were not known to the West.Researchers, teachers and graduate students in the fields of electrical and mechanical engineering, physics, chemistry, biology, economics will find this book most useful. Applied mathematicians and control engineers from various fields of technology dealing with complex oscillatory systems will also benefit from it.
Bifurcation and Chaos in Nonsmooth Mechanical Systems
Author: Jan Awrejcewicz
Publisher: World Scientific
Published: 2003
Total Pages: 564
ISBN-13: 9812384596
DOWNLOAD EBOOKThis book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical and computational developments.
Regular and Chaotic Oscillations
Author: Polina S. Landa
Publisher: Springer Science & Business Media
Published: 2001-04-01
Total Pages: 424
ISBN-13: 9783540410010
DOWNLOAD EBOOKThis text maps out the modern theory of non-linear oscillations. The material is presented in a non-traditional manner and emphasises the new results of the theory - obtained partially by the author, who is one of the leading experts in the area. Among the topics are: synchronization and chaotization of self-oscillatory systems and the influence of weak random vibration on modification of characteristics and behaviour of the non-linear systems.
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
Author: John Guckenheimer
Publisher: Springer Science & Business Media
Published: 2013-11-21
Total Pages: 475
ISBN-13: 1461211409
DOWNLOAD EBOOKAn application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.
Nonlinear Dynamics and Chaos
Author: Steven H. Strogatz
Publisher: CRC Press
Published: 2018-05-04
Total Pages: 532
ISBN-13: 0429961111
DOWNLOAD EBOOKThis textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Bifurcation and Chaos in Simple Dynamical Systems
Author: Jan Awrejcewicz
Publisher: World Scientific
Published: 1989
Total Pages: 148
ISBN-13: 9789810200381
DOWNLOAD EBOOKThis book presents a detailed analysis of bifurcation and chaos in simple non-linear systems, based on previous works of the author. Practical examples for mechanical and biomechanical systems are discussed. The use of both numerical and analytical approaches allows for a deeper insight into non-linear dynamical phenomena. The numerical and analytical techniques presented do not require specific mathematical knowledge.
IUTAM Symposium on Interaction between Dynamics and Control in Advanced Mechanical Systems
Author: Dick H. van Campen
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 458
ISBN-13: 9401157782
DOWNLOAD EBOOKDuring the last decades, applications of dynamical analysis in advanced, often nonlinear, engineering systems have been evolved in a revolutionary way. In this context one can think of applications in aerospace engineering like satellites, in naval engineering like ship motion, in mechanical engineering like rotating machinery, vehicle systems, robots and biomechanics, and in civil engineering like earthquake dynamics and offshore technology. One could continue with this list for a long time. The application of advanced dynamics in the above fields has been possible due to the use of sophisticated computational techniques employing powerful concepts of nonlinear dynamics. These concepts have been and are being developed in mathematics, mechanics and physics. It should be remarked that careful experimental studies are vitally needed to establish the real existence and observability of the predicted dynamical phenomena. The interaction between nonlinear dynamics and nonlinear control in advanced engineering systems is becoming of increasing importance because of several reasons. Firstly, control strategies in nonlinear systems are used to obtain desired dynamic behaviour and improved reliability during operation, Applications include power plant rotating machinery, vehicle systems, robotics, etc. Terms like motion control, optimal control and adaptive control are used in this field of interest. Since mechanical and electronic components are often necessary to realize the desired action in practice, the engineers use the term mechatronics to indicate this field. If the desired dynamic behaviour is achieved by changing design variables (mostly called system parameters), one can think of fields like control of chaos.
Chaos in Structural Mechanics
Author: Jan Awrejcewicz
Publisher: Springer Science & Business Media
Published: 2009-11-11
Total Pages: 424
ISBN-13: 3540776761
DOWNLOAD EBOOKThis volume introduces new approaches to modeling strongly nonlinear behaviour of structural mechanical units: beams, plates and shells or composite systems. The text draws on bifurcation theory and chaos, emphasizing control and stability of objects and systems.
