Nonholonomic Motion of Rigid Mechanical Systems from a DAE Viewpoint

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. Several issues are investigated in depth to provide a sound and complete justification of the DAE model. These issues include the development of a generalized Gauss principle of least constraint, a study of the effect of the failure of an important full-rank condition, and a precise characterization of the state spaces.

Patrick J. Rabier is Professor of Mathematics at the University of Pittsburgh. He is the author of five books and over 70 articles in functional analysis, numerical analysis, partial differential equations, and differential-algebraic equations. Werner C. Rheinboldt is Professor Emeritus at the University of Pittsburgh; he was Andrew Mellon Professor of Mathematics there from 1978-1998. He is the author of five books and more than 130 articles in the areas of numerical analysis, computer science, engineering applications, ordinary and partial differential equations, and differential-algebraic equations.