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The lectures in this 2005 book are intended to bring young researchers to the current frontier of knowledge in geometrical mechanics and dynamical systems. They succinctly cover an unparalleled range of topics from the basic concepts of symplectic and Poisson geometry, through integrable systems, KAM theory, fluid dynamics, and symmetric bifurcation theory. The lectures are based on summer schools for graduate students and postdocs and provide complementary and contrasting viewpoints of key topics: the authors cut through an overwhelming amount of literature to show young mathematicians how to get to the core of the various subjects and thereby enable them to embark on research careers.

Mechanics, Analytic. --- Geometry, Differential. --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Differential geometry --- Analytical mechanics --- Kinetics

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In his great work, Mecanique Analytique (1788)-^Lagrange used the term "analytical" to mean "non-geometrical." Indeed, Lagrange made the following boast: "No diagrams will be found in this work. The methods that I explain in it require neither constructions nor geometrical or mechanical arguments, but only the algebraic operations inherent to a regular and uniform process. Those who love Analysis will, with joy, see mechanics become a new branch of it and will be grateful to me for thus having extended its field." This was in marked contrast to Newton's Philosophiae Naturalis Principia Mathematica (1687) which is full of elaborate geometrical constructions. It has been remarked that the classical Greeks would have understood some of the Principia but none of the Mecanique Analytique. The term analytical dynamics has now come to mean the develop­ments in dynamics from just after Newton to just before the advent of relativity theory and quantum mechanics, and it is this meaning of the term that is meant here. Frequent use will be made of diagrams to illus­trate the theory and its applications, although it will be noted that as the book progresses and the material gets "more analytical", the number of figures per chapter tends to decrease, although not monotonically.

Dynamics. --- Mechanics, Applied. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Engineering. --- Vibration. --- Engineering, general. --- Vibration, Dynamical Systems, Control. --- Cycles --- Sound --- Construction --- Industrial arts --- Technology --- Dynamical systems.

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This book provides an overview of the theory of stability analysis and its applications. It is focused on various methods devoted to analyzing wheeled vehicle behavior. The authors provide both basic and advanced knowledge of the subject. This book summarizes their research experience and extensive teaching. A large number of practical examples are included throughout to help readers understand the theory introduced. The book has several original features: • The stability analysis of nonlinear systems that is carried out utilizes the definitions of stability in the sense of Lapunov ("mathematical stability") and the definitions of stability in the sense of Bogusz ("technical stability"). • The book emphasizes stability analysis of wheeled vehicles and their systems. • Computer-aided methods for investigations of wheeled vehicle behaviors are discussed. Audience This book is intended for both undergraduate and graduate students, academics, researchers in mechanics and dynamics, nonlinear scientists, applied mathematicians, engineers, and automobile experts.

Dynamics. --- Motor vehicles --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Stability. --- Automotive vehicles --- Transportation, Automotive --- Vehicles --- Vibration. --- Engineering. --- Vibration, Dynamical Systems, Control. --- Automotive Engineering. --- Construction --- Industrial arts --- Technology --- Cycles --- Sound --- Dynamical systems. --- Automotive engineering.

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Computer Science --- Differentiable dynamical systems --- Economics --- Mathematical optimization --- Matrix theory --- Operations research --- Differential geometry. Global analysis

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This monograph presents a reasonably rigorous theory of a highly relevant chaos control method: suppression-enhancement of chaos by weak periodic excitations in low-dimensional, dissipative and non-autonomous systems. The theory provides analytical estimates of the ranges of parameters of the chaos-controlling excitation for suppression-enhancement of the initial chaos. The important applications of the theory presented in the book include: (1) control of chaotic escape from a potential well; (2) suppression of chaos in a driven Josephson junction; (3) control of chaotic solitons in Frenkel-Ko

Chaotic behavior in systems. --- Differentiable dynamical systems. --- Nonlinear control theory. --- Control theory --- Nonlinear theories --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- Dynamics --- System theory