Contemporary Mathematics 1989; 468 pp; softcover Volume: 97 Reprint/Revision History: reprinted 1992 ISBN10: 0821851047 ISBN13: 9780821851043 List Price: US$67 Member Price: US$53.60 Order Code: CONM/97
 The study of complex, interconnected mechanical systems with rigid and flexible articulated components is of growing interest to both engineers and mathematicians. Recent work in this area reveals a rich geometry underlying the mathematical models used in this context. In particular, Lie groups of symmetries, reduction, and Poisson structures play a significant role in explicating the qualitative properties of multibody systems. In engineering applications, it is important to exploit the special structures of mechanical systems. For example, certain mechanical problems involving control of interconnected rigid bodies can be formulated as LiePoisson systems. The dynamics and control of robotic, aeronautic, and space structures involve difficulties in modeling, mathematical analysis, and numerical implementation. For example, a new generation of spacecraft with large, flexible components are presenting new challenges to the accurate modeling and prediction of the dynamic behavior of such structures. Recent developments in Hamiltonian dynamics and coupling of systems with symmetries has shed new light on some of these issues, while engineering questions have suggested new mathematical structures. These kinds of considerations motivated the organization of the AMSIMSSIAM Joint Summer Research Conference on Control Theory and Multibody Systems, held at Bowdoin College in August, 1988. This volume contains the proceedings of that conference. The papers presented here cover a range of topics, all of which could be viewed as applications of geometrical methods to problems arising in dynamics and control. The volume contains contributions from some of the top researchers and provides an excellent overview of the frontiers of research in this burgeoning area. Table of Contents  J. Baillieul  An enumerative theory of equilibrium rotations for planar kinematic chains
 A. M. Bloch and R. R. Ryan  Stability and stiffening of driven and free planar rotating beams
 P. E. Crouch and A. Van der Shaft  Characterization of Hamiltonian inputoutput systems
 R. F. Curtain  Robustness of distributed parameter systems
 C. J. Damaren and G. M. T. D'Eleuterio  On the relationship between discretetime optimal control and recursive dynamics for elastic multibody chains
 T. E. Duncan  Some solvable stochastic control problems in compact symmetric spaces of rank one
 T. A. W. Dwyer III  Slewinduced deformation shaping on slow integral manifolds
 B. Gardner, W. F. Shadwick, and G. R. Wilkens  Feedback equivalence and symmetries of Brunowski normal forms
 D. E. Koditschek  The application of total energy as a Lyapunov function for mechanical control systems
 J. Koiller  Classical adiabatic angles for slowly moving mechanical systems
 P. S. Krishnaprasad  Eulerian manybody problems
 M. Levi  Morse theory for a model space structure
 Z. Li and S. Sastry  A unified approach for the control of multifingered robot hands
 D.C. Liaw and E. H. Abed  Tethered satellite system stability
 E. B. Lin  Quantum control theory I
 J. E. Marsden, R. Montgomery, and T. Ratiu  CartanHannayBerry Phases and symmetry
 J. E. Marsden, J. C. Simo, D. Lewis, and T. A. Posbergh  Block diagonalization and the energymomentum method
 G. Patrick  The dynamics of two coupled rigid bodies in three space
 E. Polak  Nonsmooth optimization algorithms for the design of controlled flexible structures
 T. A. Posbergh, J. C. Simo, and J. E. Marsden  Stability analysis of a rigid body with attached geometrically nonlinear rod by the energymomentum method
 G. S. de Alvarez  Controllability of Poisson control systems with symmetries
 J. Scheurle  Chaos in a rapidly forced pendulum equation
 N. Sreenath  Accurate time critical control of many body systems
 A. J. van der Schaft  Hamiltonian control systems: decomposition and clamped dynamics
 J. Wittenburg  Graphtheoretical methods in multibody dynamics
