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This second edition provides much-needed updates to the original volume. Like the first edition, it emphasizes the ideas behind the algorithms as well as their theoretical foundations and properties, rather than focusing strictly on computational details; at the same time, this new version is now largely self-contained and includes essential proofs. Additions have been made to almost every chapter, including an introduction to the theory of inexact Newton methods, a basic theory of continuation methods in the setting of differentiable manifolds, and an expanded discussion of minimization...

This book contains a unique description of the nonholonomic motion of systems of rigid bodies by differential algebraic systems. Nonholonomic Motion of Rigid Mechanical Systems from a DAE Viewpoint focuses on rigid body systems subjected to kinematic constraints (constraints that depend on the velocities of the bodies, e.g., as they arise for nonholonomic motions) and discusses in detail how the equations of motion are developed. The authors show that such motions can be modeled in terms of differential algebraic equations (DAEs), provided only that the correct variables are introduced....

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in re- search and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numeri- cal and symbolic computer systems, dynamical...