Stability of Discrete Non-conservative Systems first exposes the general concepts and results concerning stability issues. It then presents an approach of stability that is different from Lyapunov which leads to the second order work criterion. Thanks to the new concept of Kinematic Structural Stability, a complete equivalence between two approaches of stability is obtained for a divergent type of stability. Extensions to flutter instability, to continuous systems, and to the dual questions concerning the measure of non-conservativeness provides a full, fresh look at these fundamental questions. A special chapter is devoted to applications for granular systems. - Presents a structured review on stability questions - Provides analytical methods and key concepts that may be used in non-conservative frameworks like hypoelasticity
Multi-body Kinematics and Dynamics with Lie Groups explores the use of Lie groups in the kinematics and dynamics of rigid body systems. The first chapter reveals the formal properties of Lie groups on the examples of rotation and Euclidean displacement groups. Chapters 2 and 3 show the specific algebraic properties of the displacement group, explaining why dual numbers play a role in kinematics (in the so-called screw theory). Chapters 4 to 7 make use of those mathematical tools to expound the kinematics of rigid body systems and in particular the kinematics of open and closed kinematical chains. A complete classification of their singularities demonstrates the efficiency of the method. Dynamics of multibody systems leads to very big computations. Chapter 8 shows how Lie groups make it possible to put them in the most compact possible form, useful for the design of software, and expands the example of tree-structured systems. This book is accessible to all interested readers as no previous knowledge of the general theory is required. - Presents a overview of the practical aspects of Lie groups based on the example of rotation groups and the Euclidean group - Makes it clear that the interface between Lie groups methods in mechanics and numerical calculations is very easy - Includes theoretical results that have appeared in scientific articles
The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory. The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.
Stability of Discrete Non-conservative Systems first exposes the general concepts and results concerning stability issues. It then presents an approach of stability that is different from Lyapunov which leads to the second order work criterion. Thanks to the new concept of Kinematic Structural Stability, a complete equivalence between two approaches of stability is obtained for a divergent type of stability. Extensions to flutter instability, to continuous systems, and to the dual questions concerning the measure of non-conservativeness provides a full, fresh look at these fundamental questions. A special chapter is devoted to applications for granular systems. - Presents a structured review on stability questions - Provides analytical methods and key concepts that may be used in non-conservative frameworks like hypoelasticity
Multi-body Kinematics and Dynamics with Lie Groups explores the use of Lie groups in the kinematics and dynamics of rigid body systems. The first chapter reveals the formal properties of Lie groups on the examples of rotation and Euclidean displacement groups. Chapters 2 and 3 show the specific algebraic properties of the displacement group, explaining why dual numbers play a role in kinematics (in the so-called screw theory). Chapters 4 to 7 make use of those mathematical tools to expound the kinematics of rigid body systems and in particular the kinematics of open and closed kinematical chains. A complete classification of their singularities demonstrates the efficiency of the method. Dynamics of multibody systems leads to very big computations. Chapter 8 shows how Lie groups make it possible to put them in the most compact possible form, useful for the design of software, and expands the example of tree-structured systems. This book is accessible to all interested readers as no previous knowledge of the general theory is required. - Presents a overview of the practical aspects of Lie groups based on the example of rotation groups and the Euclidean group - Makes it clear that the interface between Lie groups methods in mechanics and numerical calculations is very easy - Includes theoretical results that have appeared in scientific articles
Excerpts from the novels, plays, and poems of the French convict, prostitute, and literary artist join notes from his film, The Penal Colony, letters, essays, and a rare interview, all edited by a contemporary biographer.
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