Nonholonomic mechanics and control:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Springer
2003
|
| Series: | Interdisciplinary applied mathematics
24 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index. |
| Physical Description: | XIX, 483 S. Ill. |
| ISBN: | 0387955356 |
Staff View
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| 100 | 1 | |a Bloch, Anthony M. |d 1955- |e Verfasser |0 (DE-588)124711820 |4 aut | |
| 245 | 1 | 0 | |a Nonholonomic mechanics and control |c A. M. Bloch. With the collaboration of J. Baillieul, P. Crouch, and J. Marsden ; with scientific input from P.S. Krishnaprasad, R.M. Murray, and D. Zenkov |
| 264 | 1 | |a New York u.a. |b Springer |c 2003 | |
| 300 | |a XIX, 483 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Interdisciplinary applied mathematics |v 24 | |
| 500 | |a Includes bibliographical references and index. | ||
| 650 | 4 | |a Mechanisches System - Nichtholonome Bedingung - Nichtlineare Kontrolltheorie | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Nonholonomic dynamical systems | |
| 650 | 0 | 7 | |a Nichtlineare Kontrolltheorie |0 (DE-588)4475218-0 |2 gnd |9 rswk-swf |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface v
About the Authors xi
A Diagram for the Book xvii
1 Introduction 1
1.1 Generalized Coordinates and Newton Euler Balance ... 2
1.2 Hamilton s Principle 6
1.3 The Lagrange d Alembert Principle 11
1.4 The Vertical Rolling Disk 15
1.5 The Falling Rolling Disk 21
1.6 The Knife Edge 23
1.7 The Chaplygin Sleigh 25
1.8 The Heisenberg System 29
1.9 The Rigid Body 34
1.10 The Roller Racer 42
1.11 The Rattleback 43
1.12 The Toda Lattice 45
2 Mathematical Preliminaries 49
2.1 Vector Fields, Flows, and Differential Equations 49
2.2 Differentiable Manifolds 62
2.3 Stability 71
xiv Contents
2.4 Center Manifold 74
2.5 Differential Forms 79
2.6 Lie Derivatives 86
2.7 Stokes s Theorem, Riemannian Manifolds, Distributions . 93
2.8 Lie Groups 97
2.9 Fiber Bundles and Connections 105
3 Basic Concepts in Geometric Mechanics 119
3.1 Symplectic and Poisson Manifolds and Hamiltonian Flows 120
3.2 Cotangent Bundles 123
3.3 Lagrangian Mechanics and Variational Principles 124
3.4 Mechanical Systems with External Forces 128
3.5 Lie Poisson Brackets and the Rigid Body 130
3.6 The Euler Poincare Equations 134
3.7 Momentum Maps 136
3.8 Symplectic and Poisson Reduction 139
3.9 A Particle in a Magnetic Field 142
3.10 The Mechanical Connection 144
3.11 The Lagrange Poincare Equations 146
3.12 The Energy Momentum Method 150
3.13 Coupled Planar Rigid Bodies 158
3.14 Phases and Holonomy, the Planar Skater 167
4 Introduction to Aspects of Geometric Control Theory 175
4.1 Nonlinear Control Systems 175
4.2 Controllability and Accessibility 177
4.3 Representation of System Trajectories 182
4.4 Averaging and Trajectory Planning 190
4.5 Stabilization 194
4.6 Hamiltonian and Lagrangian Control Systems 198
5 Nonholonomic Mechanics 207
5.1 Equations of Motion 211
5.2 The Lagrange d Alembert Principle 216
5.3 Projected Connections and Newton s Law 221
5.4 Systems with Symmetry 223
5.5 The Momentum Equation 228
5.6 Examples of the Nonholonomic Momentum Map 238
5.7 More General Nonholonomic Systems with Symmetries . . 248
5.8 Poisson Geometry of Nonholonomic Systems 254
6 Control of Mechanical and Nonholonomic Systems 277
6.1 Background in Kinematic Nonholonomic Control Systems 277
6.2 Stabilization of the Heisenberg System 285
6.3 Stabilization of a Generalized Heisenberg System 291
Contents xv
6.4 Controllability, Accessibility, and Stabilizability 301
6.5 Smooth Stabilization to a Manifold 304
6.6 Nonsmooth Stabilization 308
6.7 Nonholonomic Systems on Riemannian Manifolds 319
7 Optimal Control 329
7.1 Variational Nonholonomic Problems 329
7.2 Optimal Control and the Maximum Principle 336
7.3 Variational Nonholonomic Systems and Optimal Control . 339
7.4 Kinematic Sub Riemannian Optimal Control Problems . . 342
7.5 Optimal Control and a Particle in a Magnetic Field .... 353
7.6 Optimal Control of Mechanical Systems 358
8 Stability of Nonholonomic Systems 367
8.1 The Nonholonomic Energy Momentum Method 367
8.2 Overview 370
8.3 The Pure Transport Case 372
8.4 The Nonpure Transport Case 377
8.5 General Case—the Lyapunov Malkin Method 387
8.6 Euler Poincare Suslov Equations 392
9 Energy Based Methods for Stabilization 399
9.1 Controlled Lagrangian Methods 399
9.2 Feedback Design and Matching 402
9.3 Stabilization of a Class of Nonholonomic Systems 410
9.4 Averaging for Controlled Lagrangian Systems 415
9.5 Dynamic Nonholonomic Averaging 435
References 439
Index 471
|
| any_adam_object | 1 |
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| dewey-full | 514.74 |
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| dewey-ones | 514 - Topology |
| dewey-raw | 514.74 |
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014936397 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:08:43Z |
| institution | BVB |
| isbn | 0387955356 |
| language | English |
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| physical | XIX, 483 S. Ill. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
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| publisher | Springer |
| record_format | marc |
| series | Interdisciplinary applied mathematics |
| series2 | Interdisciplinary applied mathematics |
| spelling | Bloch, Anthony M. 1955- Verfasser (DE-588)124711820 aut Nonholonomic mechanics and control A. M. Bloch. With the collaboration of J. Baillieul, P. Crouch, and J. Marsden ; with scientific input from P.S. Krishnaprasad, R.M. Murray, and D. Zenkov New York u.a. Springer 2003 XIX, 483 S. Ill. txt rdacontent n rdamedia nc rdacarrier Interdisciplinary applied mathematics 24 Includes bibliographical references and index. Mechanisches System - Nichtholonome Bedingung - Nichtlineare Kontrolltheorie Control theory Nonholonomic dynamical systems Nichtlineare Kontrolltheorie (DE-588)4475218-0 gnd rswk-swf Mechanik (DE-588)4038168-7 gnd rswk-swf Nichtholonome Bedingung (DE-588)4171735-1 gnd rswk-swf Mechanisches System (DE-588)4132811-5 gnd rswk-swf Nichtholonome Bedingung (DE-588)4171735-1 s Nichtlineare Kontrolltheorie (DE-588)4475218-0 s Mechanik (DE-588)4038168-7 s Mechanisches System (DE-588)4132811-5 s 1\p DE-604 Interdisciplinary applied mathematics 24 (DE-604)BV004216726 24 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010079981&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bloch, Anthony M. 1955- Nonholonomic mechanics and control Interdisciplinary applied mathematics Mechanisches System - Nichtholonome Bedingung - Nichtlineare Kontrolltheorie Control theory Nonholonomic dynamical systems Nichtlineare Kontrolltheorie (DE-588)4475218-0 gnd Mechanik (DE-588)4038168-7 gnd Nichtholonome Bedingung (DE-588)4171735-1 gnd Mechanisches System (DE-588)4132811-5 gnd |
| subject_GND | (DE-588)4475218-0 (DE-588)4038168-7 (DE-588)4171735-1 (DE-588)4132811-5 |
| title | Nonholonomic mechanics and control |
| title_auth | Nonholonomic mechanics and control |
| title_exact_search | Nonholonomic mechanics and control |
| title_full | Nonholonomic mechanics and control A. M. Bloch. With the collaboration of J. Baillieul, P. Crouch, and J. Marsden ; with scientific input from P.S. Krishnaprasad, R.M. Murray, and D. Zenkov |
| title_fullStr | Nonholonomic mechanics and control A. M. Bloch. With the collaboration of J. Baillieul, P. Crouch, and J. Marsden ; with scientific input from P.S. Krishnaprasad, R.M. Murray, and D. Zenkov |
| title_full_unstemmed | Nonholonomic mechanics and control A. M. Bloch. With the collaboration of J. Baillieul, P. Crouch, and J. Marsden ; with scientific input from P.S. Krishnaprasad, R.M. Murray, and D. Zenkov |
| title_short | Nonholonomic mechanics and control |
| title_sort | nonholonomic mechanics and control |
| topic | Mechanisches System - Nichtholonome Bedingung - Nichtlineare Kontrolltheorie Control theory Nonholonomic dynamical systems Nichtlineare Kontrolltheorie (DE-588)4475218-0 gnd Mechanik (DE-588)4038168-7 gnd Nichtholonome Bedingung (DE-588)4171735-1 gnd Mechanisches System (DE-588)4132811-5 gnd |
| topic_facet | Mechanisches System - Nichtholonome Bedingung - Nichtlineare Kontrolltheorie Control theory Nonholonomic dynamical systems Nichtlineare Kontrolltheorie Mechanik Nichtholonome Bedingung Mechanisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010079981&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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