The book covers the fundamentals of the mechanics of multibody systems, i.e., systems of interconnected rigid bodies. A geometric view is emphasized in which the techniques and algorithms are motivated by the picture of the rigid body system as a point in the multidimensional space of all possible configurations. The reader is introduced to computer algebra methods in the form of a system, called Sophia, which is implemented in the Maple symbolic manipulation system. The first chapter provides a motivational introduction to the basic principles and an introduction to Maple. Kinematics based on the idea of tangent vectors to the configuration manifold sets the stage for dynamical analysis. The latter ranges from the Lagrange and Gibbs-Appell to Kane's equations. Coverage includes nonholonomic systems and redundant variable methods. The computer algebra methods included enable the treatment of nontrivial mechanical systems and the development of efficient numerical codes for simulation.

The book covers the fundamentals of the mechanics of multibody systems, i.e., systems of interconnected rigid bodies. A geometric view is emphasized in which the techniques and algorithms are motivated by the picture of the rigid body system as a point in the multidimensional space of all possible configurations. The reader is introduced to computer algebra methods in the form of a system, called Sophia, which is implemented in the Maple symbolic manipulation system. The first chapter provides a motivational introduction to the basic principles and an introduction to Maple. Kinematics based on the idea of tangent vectors to the configuration manifold sets the stage for dynamical analysis. The latter ranges from the Lagrange and Gibbs-Appell to Kane's equations. Coverage includes nonholonomic systems and redundant variable methods. The computer algebra methods included enable the treatment of nontrivial mechanical systems and the development of efficient numerical codes for simulation.

The book first introduces the concept of nonlinear normal modes (NNMs) and their two main definitions. The fundamental differences between classical linear normal modes (LNMs) and NNMs are explained and illustrated using simple examples. Different methods for computing NNMs from a mathematical model are presented. Both advanced analytical and numerical methods are described. Particular attention is devoted to the invariant manifold and normal form theories. The book also discusses nonlinear system identification.

LINEAR and NONLINEAR INSTABILITIES in MECHANICAL SYSTEMS An in-depth insight into nonlinear analysis and control As mechanical systems become lighter, faster, and more flexible, various nonlinear instability phenomena can occur in practical systems. The fundamental knowledge of nonlinear analysis and control is essential to engineers for analysing and controlling nonlinear instability phenomena. This book bridges the gap between the mathematical expressions of nonlinear dynamics and the corresponding practical phenomena. Linear and Nonlinear Instabilities in Mechanical Systems: Analysis, Control and Application provides a detailed and informed insight into the fundamental methods for analysis and control for nonlinear instabilities from the practical point of view. Key features: Refers to the behaviours of practical mechanical systems such as aircraft, railway vehicle, robot manipulator, micro/nano sensor Enhances the rigorous and practical understanding of mathematical methods from an engineering point of view The theoretical results obtained by nonlinear analysis are interpreted by using accompanying videos on the real nonlinear behaviors of nonlinear mechanical systems Linear and Nonlinear Instabilities in Mechanical Systems is an essential textbook for students on engineering courses, and can also be used for self-study or reference by engineers.

A modern mechanical structure must work at high speed and with high precision in space and time, in cooperation with other machines and systems. All this requires accurate dynamic modelling, for instance, recognizing Coriolis and centrifugal forces, strong coupling effects, flexibility of links, large angles articulation. This leads to a motion equation which must be highly nonlinear to describe the reality. r1oreover, work on the manufacturing floor requires coordination between nachines, between each machine and a conveyor, and demands robustness of the controllers against uncertainty in payload, gravity, external perturbations etc. This requires adaptive controllers and system coordination, and perhaps a self organizing structure. The machines become complex, strongly nonlinear and strongly coupled mechanical systems with many degrees of freedom, controlled by sophisticated mathematical programs. The design of such systems needs basic research in Control and System Dynamics, as well as in Decision Making Theory (Dynamic Games), not only in the use of these disciplines, but in their adjustment to the present demand. This in turn generates the need to prepare engineering students for the job by the teaching of more sophisti cated techniques in control and Mechanics than those contained in previous curricula. On the other hand, all that was mentioned above regarding the design of machines applies equally well to other presently designed and used mechan ical structures or systems.

When M. Vidyasagar wrote the first edition of Nonlinear Systems Analysis, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic techniques because virtually all physical systems are nonlinear in nature. The second edition, now republished in SIAM's Classics in Applied Mathematics series, provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. It develops nonlinear generalizations of a large number of techniques and methods widely used in linear control theory. The book contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. Audience: this text is designed for use at the graduate level in the area of nonlinear systems and as a resource for professional researchers and practitioners working in areas such as robotics, spacecraft control, motor control, and power systems.