Author : Jan Awrejcewicz
Publisher : World Scientific
Page : 566 pages
File Size : 37,20 MB
Release : 2003
Category : Mathematics
ISBN : 9789812564801
This book presents the theoretical frame for studying lumped nonsmoothdynamical systems: the mathematical methods are recalled, and adaptednumerical methods are introduced (differential inclusions, maximalmonotone operators, Filippov theory, Aizerman theory, etc.
Author : Jan Awrejcewicz
Publisher : World Scientific
Page : 564 pages
File Size : 11,99 MB
Release : 2003-07-14
Category : Mathematics
ISBN : 9814485403
This 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.
Author : Remco I. Leine
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 11,43 MB
Release : 2013-03-19
Category : Mathematics
ISBN : 3540443983
This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.
Author : Jan Awrejcewicz
Publisher : Springer
Page : 621 pages
File Size : 18,93 MB
Release : 2014-09-17
Category : Mathematics
ISBN : 3319076590
This book applies a step-by-step treatment of the current state-of-the-art of ordinary differential equations used in modeling of engineering systems/processes and beyond. It covers systematically ordered problems, beginning with first and second order ODEs, linear and higher-order ODEs of polynomial form, theory and criteria of similarity, modeling approaches, phase plane and phase space concepts, stability optimization and ending on chaos and synchronization. Presenting both an overview of the theory of the introductory differential equations in the context of applicability and a systematic treatment of modeling of numerous engineering and physical problems through linear and non-linear ODEs, the volume is self-contained, yet serves both scientific and engineering interests. The presentation relies on a general treatment, analytical and numerical methods, concrete examples and engineering intuition. The scientific background used is well balanced between elementary and advanced level, making it as a unique self-contained source for both theoretically and application oriented graduate and doctoral students, university teachers, researchers and engineers of mechanical, civil and mechatronic engineering.
Author : Jan Awrejcewicz
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 20,47 MB
Release : 2008-12-10
Category : Mathematics
ISBN : 0387096531
This work is devoted to an intensive study in contact mechanics, treating the nonsmooth dynamics of contacting bodies. Mathematical modeling is illustrated and discussed in numerous examples of engineering objects working in different kinematic and dynamic environments. Topics covered in five self-contained chapters examine non-steady dynamic phenomena which are determined by key factors: i.e., heat conduction, thermal stresses, and the amount of wearing. New to this monograph is the importance of the inertia factor, which is considered on par with thermal stresses. Nonsmooth Dynamics of Contacting Thermoelastic Bodies is an engaging accessible practical reference for engineers (civil, mechanical, industrial) and researchers in theoretical and applied mechanics, applied mathematics, physicists, and graduate students.
Author : Vladimir Nikolov Damgov
Publisher : World Scientific
Page : 574 pages
File Size : 23,71 MB
Release : 2004-11-22
Category : Science
ISBN : 9814497738
The book comprises a broad panorama of phenomena occurring in four major classes of radiophysical and mechanical systems — linear, nonlinear, parametric, and nonlinear-parametric. An analytical technique for the broad circle of issues under consideration is developed. It is presented in a user-friendly form, allowing its further direct application in research practices.Analytical methods are presented for investigating modulation-parametric and nonlinear systems, oscillating systems with periodic and almost periodic time-dependent parameters, effects of adaptive self-organization in coupled resonance systems and oscillating systems under the action of external forces, nonlinear with respect to the coordinates of excited systems.Of an interdisciplinary nature, this volume can serve as a handbook for developing lecture courses such as Fundamentals of Nonlinear Dynamics and Theory of Nonlinear Oscillations, Theory of Nonlinear Circuits and Systems, Fundamentals of Radiophysics and Electronics, Theory of Signals and Theoretical Radiophysics, Theoretical Mechanics and Electrodynamics.
Author : Jan Awrejcewicz
Publisher : World Scientific
Page : 318 pages
File Size : 50,10 MB
Release : 2007-09-21
Category : Science
ISBN : 9814474649
This book focuses on the development of Melnikov-type methods applied to high dimensional dynamical systems governed by ordinary differential equations. Although the classical Melnikov's technique has found various applications in predicting homoclinic intersections, it is devoted only to the analysis of three-dimensional systems (in the case of mechanics, they represent one-degree-of-freedom nonautonomous systems). This book extends the classical Melnikov's approach to the study of high dimensional dynamical systems, and uses simple models of dry friction to analytically predict the occurrence of both stick-slip and slip-slip chaotic orbits, research which is very rarely reported in the existing literature even on one-degree-of-freedom nonautonomous dynamics.This pioneering attempt to predict the occurrence of deterministic chaos of nonlinear dynamical systems will attract many researchers including applied mathematicians, physicists, as well as practicing engineers. Analytical formulas are explicitly formulated step-by-step, even attracting potential readers without a rigorous mathematical background.
Author : Hendrik Nijmeijer
Publisher : World Scientific
Page : 219 pages
File Size : 33,48 MB
Release : 2003
Category : Technology & Engineering
ISBN : 981238605X
The main goal of this book is to prove analytically and validate experimentally that synchronization in multi-composed mechanical systems can be achieved in the case of partial knowledge of the state vector of the systems, i.e. when only positions are measured. For this purpose, synchronization schemes based on interconnections between the systems, feedback controllers and observers are proposed. Because mechanical systems include a large variety of systems, and since it is impossible to address all of them, the book focuses on robot manipulators. Nonetheless the ideas developed here can be extended to other mechanical systems, such as mobile robots, motors and generators.
Author : Mario Bernardo
Publisher : Springer Science & Business Media
Page : 497 pages
File Size : 50,6 MB
Release : 2008-01-01
Category : Mathematics
ISBN : 1846287081
This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.
Author : Bram De Kraker
Publisher : World Scientific
Page : 462 pages
File Size : 44,40 MB
Release : 2000-04-28
Category : Technology & Engineering
ISBN : 9814497908
Rapid 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.
