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Your search keyword '"Bloch, A.M."' showing total 14 results
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14 results on '"Bloch, A.M."'

2. Nonholonomic Mechanics and Control / by A.M. Bloch ; edited by P. S. Krishnaprasad, R.M. Murray.

Author

Bloch, A.M. author., Krishnaprasad, P. S. editor., Murray, R.M. editor., SpringerLink (Online service), Bloch, A.M. author., Krishnaprasad, P. S. editor., Murray, R.M. editor., and SpringerLink (Online service)

Abstract

This book explores some of the connections between control theory and geometric mechanics; that is, control theory is linked with a geometric view of classical mechanics in both its Lagrangian and Hamiltonian formulations and in particular with the theory of mechanical systems subject to motion constraints. The synthesis of the topic is appropriate as there is a particularly rich connection between mechanics and nonlinear control theory. The book provides a unified treatment of nonlinear control theory and constrained mechanical systems and illustrates the elegant mathematics behind manysimple, interesting, and useful mechanical examples.It is intended for graduate students who wish to learn this subject and researchers in the area who want to enhance their techniques. The bookcontainssections focusing on physical examples and elementary terms, as well as theoretical sections that use sophisticated analysis and geometry. The first four chapters offer preliminaries and background information, while the remaining fiveare broken down into chapters on nonholonomic mechanics, control and stabilization, optimal control, energy-based, and recent energy-based techniques for mechanical and nonholonomic systems. The second edition of the book extends many of the topics discussed in the first edition to incorporate both new research and more historical background. The additional material includes work on the Hamel equations and quasivelocities, discrete dynamics, bo th holonomic and nonholonomic, Hamiltonization, and the Hamilton-Jacobi equation. In addition new examples and exercises have been added. Review of earlier Edition (A.J. van der Schaft, IEEE Control System Magazine, 2005 ) This book can beread on many different levels and has been described as a “delightful book that will be valuable for both the control community and researchers” .

Published
2015

5. Dissipation Induced Instabilities.

Author

Bloch, A.M., Krishnaprasad, P.S., Marsden, J.E., and Ratiu, T.S.

Subjects
*STABILITY theory, *ENERGY dissipation, *CASIMIR effect, *HAMILTONIAN systems, *NONLINEAR theories, *SYMMETRY groups
Abstract

The main goal of this paper is to prove that if the energy-momentum (or energy-Casimir) method predicts formal instability of a relative equilibrium in a Hamiltonian system with symmetry, then with the addition of dissipation, the relative equilibrium becomes spectrally and hence linearly and nonlinearly unstable. The energy-momentum method assumes that one is in the context of a mechanical system with a given symmetry group. Our result assumes that the dissipation chosen does not destroy the conservation law associated with the given symmetry group – thus, we consider internal dissipation. This also includes the special case of systems with no symmetry and ordinary equilibria. The theorem is proved by combining the techniques of Chetaev, who proved instability theorems using a special Chetaev-Lyapunov function, with those of Hahn, which enable one to strengthen the Chetaev results from Lyapunov instability to spectral instability. The main achievement is to strengthen Chetaev’s methods to the context of the block diagonalization version of the energy momentum method given by Lewis, Marsden, Posbergh, and Simo. However, we also give the eigenvalue movement formulae of Krein, MacKay and others both in general and adapted to the context of the normal form of the linearized equations given by the block diagonal form, as provided by the energy-momentum method. A number of specific examples, such as the rigid body with internal rotors, are provided to illustrate the results. [ABSTRACT FROM AUTHOR]

Published
2016
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6. Mathematical Preliminaries

Author

Bloch, Anthony M., Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Holmes, Philip, Editor-in-chief, Glass, Leon, Series editor, Kohn, Robert, Series editor, Krishnaprasad, P. S., Series editor, Murray, James D., Series editor, Sastry, Shankar, Series editor, Sneyd, James, Series editor, Bloch, A.M., and Murray, R.M., editor

Published
2015
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7. Energy-Based Methods for Stabilization of Controlled Lagrangian Systems

Author

Bloch, Anthony M., Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Holmes, Philip, Editor-in-chief, Glass, Leon, Series editor, Kohn, Robert, Series editor, Krishnaprasad, P. S., Series editor, Murray, James D., Series editor, Sastry, Shankar, Series editor, Sneyd, James, Series editor, Bloch, A.M., and Murray, R.M., editor

Published
2015
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8. Stability and Structure of Nonholonomic Systems

Author

Bloch, Anthony M., Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Holmes, Philip, Editor-in-chief, Glass, Leon, Series editor, Kohn, Robert, Series editor, Krishnaprasad, P. S., Series editor, Murray, James D., Series editor, Sastry, Shankar, Series editor, Sneyd, James, Series editor, Bloch, A.M., and Murray, R.M., editor

Published
2015
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9. Optimal Control

Author

Bloch, Anthony M., Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Holmes, Philip, Editor-in-chief, Glass, Leon, Series editor, Kohn, Robert, Series editor, Krishnaprasad, P. S., Series editor, Murray, James D., Series editor, Sastry, Shankar, Series editor, Sneyd, James, Series editor, Bloch, A.M., and Murray, R.M., editor

Published
2015
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10. Nonholonomic Mechanics

Author

Bloch, Anthony M., Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Holmes, Philip, Editor-in-chief, Glass, Leon, Series editor, Kohn, Robert, Series editor, Krishnaprasad, P. S., Series editor, Murray, James D., Series editor, Sastry, Shankar, Series editor, Sneyd, James, Series editor, Bloch, A.M., and Murray, R.M., editor

Published
2015
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11. An Introduction to Aspects of Geometric Control Theory

Author

Bloch, Anthony M., Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Holmes, Philip, Editor-in-chief, Glass, Leon, Series editor, Kohn, Robert, Series editor, Krishnaprasad, P. S., Series editor, Murray, James D., Series editor, Sastry, Shankar, Series editor, Sneyd, James, Series editor, Bloch, A.M., and Murray, R.M., editor

Published
2015
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12. Control of Mechanical and Nonholonomic Systems

Author

Bloch, Anthony M., Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Holmes, Philip, Editor-in-chief, Glass, Leon, Series editor, Kohn, Robert, Series editor, Krishnaprasad, P. S., Series editor, Murray, James D., Series editor, Sastry, Shankar, Series editor, Sneyd, James, Series editor, Bloch, A.M., and Murray, R.M., editor

Published
2015
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13. Basic Concepts in Geometric Mechanics

Author

Bloch, Anthony M., Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Holmes, Philip, Editor-in-chief, Glass, Leon, Series editor, Kohn, Robert, Series editor, Krishnaprasad, P. S., Series editor, Murray, James D., Series editor, Sastry, Shankar, Series editor, Sneyd, James, Series editor, Bloch, A.M., and Murray, R.M., editor

Published
2015
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14. Introduction

Author

Bloch, Anthony M., Antman, Stuart, Editor-in-chief, Greengard, Leslie, Editor-in-chief, Holmes, Philip, Editor-in-chief, Glass, Leon, Series editor, Kohn, Robert, Series editor, Krishnaprasad, P. S., Series editor, Murray, James D., Series editor, Sastry, Shankar, Series editor, Sneyd, James, Series editor, Bloch, A.M., and Murray, R.M., editor

Published
2015
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