Qualitative Analysis of Nonsmooth Dynamics

Qualitative Analysis of Nonsmooth Dynamics: A Simple Discrete System with Unilateral Contact and Coulomb Friction explores the effects of small and large deformations to understand how shocks, sliding, and stick phases affect the trajectories of mechanical systems. By analyzing these non-regularities successively this work explores the set of equilibria and properties of periodic solutions of elementary mechanical systems, where no classical results issued from the theory of ordinary differential equations are readily available, such as stability, continuation or approximation of solutions. The authors focus on unilateral contact in presence of Coulomb friction and show, in particular, how any regularization would greatly simplify the mathematics but lead to unacceptable physical responses. Explores the effects of small and large deformations to understand how shocks, sliding, and stick phases affect the trajectories of mechanical systems Includes theoretical results concerning the full investigation of the behavior under constant or oscillating loadings, even in the case of the simplest mechanical systems Provides a focus on unilateral contact in presence of Coulomb friction Helps you gain an accurate understanding of how the transition occurs to ensure the safe use of any machine involving rotating or sliding mechanisms

Produk Detail:

  • Author : Alain Léger
  • Publisher : Elsevier
  • Pages : 222 pages
  • ISBN : 0081012012
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKQualitative Analysis of Nonsmooth Dynamics

Qualitative Analysis of Nonsmooth Dynamics

Qualitative Analysis of Nonsmooth Dynamics
  • Author : Alain Léger,Elaine Pratt
  • Publisher : Elsevier
  • Release : 26 April 2016
GET THIS BOOKQualitative Analysis of Nonsmooth Dynamics

Qualitative Analysis of Nonsmooth Dynamics: A Simple Discrete System with Unilateral Contact and Coulomb Friction explores the effects of small and large deformations to understand how shocks, sliding, and stick phases affect the trajectories of mechanical systems. By analyzing these non-regularities successively this work explores the set of equilibria and properties of periodic solutions of elementary mechanical systems, where no classical results issued from the theory of ordinary differential equations are readily available, such as stability, continuation or approximation of

A Smooth and Discontinuous Oscillator

A Smooth and Discontinuous Oscillator
  • Author : Qingjie Cao,Alain Léger
  • Publisher : Springer
  • Release : 27 September 2016
GET THIS BOOKA Smooth and Discontinuous Oscillator

This is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD attractors discussed in this book represents a further milestone in nonlinear dynamics, following on the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963. This particular system bears significant similarities to the Duffing oscillator, exhibiting the standard

Complexity in Biological and Physical Systems

Complexity in Biological and Physical Systems
  • Author : Ricardo Lopez-Ruiz
  • Publisher : BoD – Books on Demand
  • Release : 02 May 2018
GET THIS BOOKComplexity in Biological and Physical Systems

Modeling and simulating biological and physical systems are nowadays active branches of science. The diversity and complexity of behaviors and patterns present in the natural world have their reciprocity in life systems. Bifurcations, solitons and fractals are some of these ubiquitous structures that can be indistinctively identified in many models with the most diverse applications, from microtubules with an essential role in the maintenance and the shaping of cells, to the nano/microscale structure in disordered systems determined with small-angle

Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems
  • Author : Bernold Fiedler
  • Publisher : Springer Science & Business Media
  • Release : 06 December 2012
GET THIS BOOKErgodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.

Dynamics and Bifurcations of Non-Smooth Mechanical Systems

Dynamics and Bifurcations of Non-Smooth Mechanical Systems
  • Author : Remco I. Leine,Henk Nijmeijer
  • Publisher : Springer Science & Business Media
  • Release : 19 March 2013
GET THIS BOOKDynamics and Bifurcations of Non-Smooth Mechanical Systems

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.

Nonsmooth Dynamics of Contacting Thermoelastic Bodies

Nonsmooth Dynamics of Contacting Thermoelastic Bodies
  • Author : Jan Awrejcewicz,Yuriy Pyr'yev
  • Publisher : Springer Science & Business Media
  • Release : 10 December 2008
GET THIS BOOKNonsmooth Dynamics of Contacting Thermoelastic Bodies

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

Advanced Topics in Nonsmooth Dynamics

Advanced Topics in Nonsmooth Dynamics
  • Author : Remco Leine,Vincent Acary,Olivier Brüls
  • Publisher : Springer
  • Release : 07 June 2018
GET THIS BOOKAdvanced Topics in Nonsmooth Dynamics

This book discusses emerging topics in the area of nonsmooth dynamics research, such as numerical methods for nonsmooth systems, impact laws for multi-collisions, nonlinear vibrations and control of nonsmooth systems. It documents original work of researchers at the European Network for NonSmooth Dynamics (ENNSD), which provides a cooperation platform for researchers in the field and promotes research focused on nonsmooth dynamics and its applications. Since the establishment of the network in 2012, six ENNSD symposia have been organized at different European

Stability and Convergence of Mechanical Systems with Unilateral Constraints

Stability and Convergence of Mechanical Systems with Unilateral Constraints
  • Author : Remco I. Leine,Nathan van de Wouw
  • Publisher : Springer Science & Business Media
  • Release : 29 December 2007
GET THIS BOOKStability and Convergence of Mechanical Systems with Unilateral Constraints

While the stability theory for systems with bilateral constraints is a well-established field, this monograph represents a systematic study of mechanical systems with unilateral constraints, such as unilateral contact, impact and friction. Such unilateral constraints give rise to non-smooth dynamical models for which stability theory is developed in this work. The book will be of interest to those working in the field of non-smooth mechanics and dynamics.

Mathematics And The 21st Century - Proceedings Of The International Conference

Mathematics And The 21st Century - Proceedings Of The International Conference
  • Author : A A Ashour,A-s F Obada
  • Publisher : World Scientific
  • Release : 02 April 2001
GET THIS BOOKMathematics And The 21st Century - Proceedings Of The International Conference

Contents:Millennium Lecture — Cairo, 15 January 2000 (M Atiyah)Trends for Science and Mathematics in the 21st Century (P A Griffiths)Arabic Mathematics and Rewriting the History of Mathematics (R Rashed)The Paradigm Shift in Mathematics Education: A Scenario for Change (W Ebeid)Einstein's Theory of Spacetime and Gravity (J Ehlers)Moduli Problems in Geometry (M S Narasimhan)Enumerative Geometry from the Greeks to Strings (C Procesi)Optical Solitons: Twenty-Seven Years of the Last Millennium and Three More Years of the New? (

Applied Nonlinear Dynamics and Chaos of Mechanical Systems with Discontinuities

Applied Nonlinear Dynamics and Chaos of Mechanical Systems with Discontinuities
  • Author : Marian Wiercigroch,Bram de Kraker
  • Publisher : World Scientific
  • Release : 28 April 2000
GET THIS BOOKApplied Nonlinear Dynamics and Chaos of Mechanical Systems with Discontinuities

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

Non-Smooth Dynamical Systems

Non-Smooth Dynamical Systems
  • Author : Markus Kunze
  • Publisher : Springer
  • Release : 06 May 2007
GET THIS BOOKNon-Smooth Dynamical Systems

The book provides a self-contained introduction to the mathematical theory of non-smooth dynamical problems, as they frequently arise from mechanical systems with friction and/or impacts. It is aimed at applied mathematicians, engineers, and applied scientists in general who wish to learn the subject.

Qualitative and Quantitative Analysis of Nonlinear Systems

Qualitative and Quantitative Analysis of Nonlinear Systems
  • Author : Michael Z. Zgurovsky,Pavlo O. Kasyanov
  • Publisher : Springer
  • Release : 11 July 2017
GET THIS BOOKQualitative and Quantitative Analysis of Nonlinear Systems

Here, the authors present modern methods of analysis for nonlinear systems which may occur in fields such as physics, chemistry, biology, or economics. They concentrate on the following topics, specific for such systems: (a) constructive existence results and regularity theorems for all weak solutions; (b) convergence results for solutions and their approximations; (c) uniform global behavior of solutions in time; and (d) pointwise behavior of solutions for autonomous problems with possible gaps by the phase variables. The general methodology for

Nonsmooth Mechanics

Nonsmooth Mechanics
  • Author : Bernard Brogliato
  • Publisher : Springer
  • Release : 29 February 2016
GET THIS BOOKNonsmooth Mechanics

Now in its third edition, this standard reference is a comprehensive treatment of nonsmooth mechanical systems refocused to give more prominence to issues connected with control and modelling. It covers Lagrangian and Newton–Euler systems, detailing mathematical tools such as convex analysis and complementarity theory. The ways in which nonsmooth mechanics influence and are influenced by well-posedness analysis, numerical analysis and simulation, modelling and control are explained. Contact/impact laws, stability theory and trajectory-tracking control are given detailed exposition connected

Singularity and Dynamics on Discontinuous Vector Fields

Singularity and Dynamics on Discontinuous Vector Fields
  • Author : Albert C.J. Luo
  • Publisher : Elsevier
  • Release : 07 July 2006
GET THIS BOOKSingularity and Dynamics on Discontinuous Vector Fields

This book discussed fundamental problems in dynamics, which extensively exist in engineering, natural and social sciences. The book presented a basic theory for the interactions among many dynamical systems and for a system whose motions are constrained naturally or artificially. The methodology and techniques presented in this book are applicable to discontinuous dynamical systems in physics, engineering and control. In addition, they may provide useful tools to solve non-traditional dynamics in biology, stock market and internet network et al, which