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Book DetailsFields Institute CommunicationsVolume: 1; 1993; 280 ppMSC: Primary 70; 58; 93; 49
This book contains a collection of papers presented at the Fields Institute workshop, “The Falling Cat and Related Problems,” held in March 1992. The theme of the workshop was the application of methods from geometric mechanics and mathematical control theory to problems in the dynamics and control of freely rotating systems of coupled rigid bodies and related nonholonomic mechanical systems. This book will prove useful in providing insight into this new and exciting area of research.
Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
ReadershipApplied mathematicians interested in control theory, geometric mechanics, dynamical systems, and differential geometry. Aerospace and mechanical engineers.
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Table of Contents
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Chapters
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J. Baillieul — Stable average motions of mechanical systems subject to periodic forcing
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A. Bloch and P. Crouch — Nonholonomic and Vakanomic control systems on Riemannian manifolds
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O. Bogoyavlenskij — General integrable problems of classical mechanics
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M. Enos — On an optimal control problem on $SO(3)\times SO(3)$ and the falling cat
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Z. Ge — On the cut points and conjugate points in a constrained variational problem
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M. Levi — A theorem of Poinsot, path ordered integrals, and parallel transport
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J. Marsden and J. Scheurle — The reduced Euler-Lagrange equations
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V. Modi — On the dynamics and control of the evolving space station “Freedom”
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R. Montgomery — Gauge theory of the falling cat
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R. Murray — Control of nonholonomic systems using chained form
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G. Patrick — A vectorizing momentum preserving symplectic integration algorithm
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T. Posbergh and R. Zhao — Stabilization of the uniform rotation of a rigid body by the energy-momentum method
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This book contains a collection of papers presented at the Fields Institute workshop, “The Falling Cat and Related Problems,” held in March 1992. The theme of the workshop was the application of methods from geometric mechanics and mathematical control theory to problems in the dynamics and control of freely rotating systems of coupled rigid bodies and related nonholonomic mechanical systems. This book will prove useful in providing insight into this new and exciting area of research.
Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Applied mathematicians interested in control theory, geometric mechanics, dynamical systems, and differential geometry. Aerospace and mechanical engineers.
-
Chapters
-
J. Baillieul — Stable average motions of mechanical systems subject to periodic forcing
-
A. Bloch and P. Crouch — Nonholonomic and Vakanomic control systems on Riemannian manifolds
-
O. Bogoyavlenskij — General integrable problems of classical mechanics
-
M. Enos — On an optimal control problem on $SO(3)\times SO(3)$ and the falling cat
-
Z. Ge — On the cut points and conjugate points in a constrained variational problem
-
M. Levi — A theorem of Poinsot, path ordered integrals, and parallel transport
-
J. Marsden and J. Scheurle — The reduced Euler-Lagrange equations
-
V. Modi — On the dynamics and control of the evolving space station “Freedom”
-
R. Montgomery — Gauge theory of the falling cat
-
R. Murray — Control of nonholonomic systems using chained form
-
G. Patrick — A vectorizing momentum preserving symplectic integration algorithm
-
T. Posbergh and R. Zhao — Stabilization of the uniform rotation of a rigid body by the energy-momentum method
