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Dynamics and Control of Multibody Systems
Edited by: J. E. Marsden, P. S. Krishnaprasad, and J. C. Simo
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Contemporary Mathematics
1989; 468 pp; softcover
Volume: 97
Reprint/Revision History:
reprinted 1992
ISBN-10: 0-8218-5104-7
ISBN-13: 978-0-8218-5104-3
List Price: US$67
Member Price: US$53.60
Order Code: CONM/97
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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 Lie-Poisson 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 AMS-IMS-SIAM 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 input-output systems
  • R. F. Curtain -- Robustness of distributed parameter systems
  • C. J. Damaren and G. M. T. D'Eleuterio -- On the relationship between discrete-time 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 -- Slew-induced 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 many-body 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 -- Cartan-Hannay-Berry Phases and symmetry
  • J. E. Marsden, J. C. Simo, D. Lewis, and T. A. Posbergh -- Block diagonalization and the energy-momentum 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 energy-momentum 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 -- Graph-theoretical methods in multibody dynamics
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