Geometric, control and numerical aspects of nonholonomic systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London
Springer
2002
|
| Schriftenreihe: | Lecture notes in mathematics
1793 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 219 S. graph. Darst. |
| ISBN: | 3540441549 |
Internformat
MARC
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| 100 | 1 | |a Cortés Monforte, Jorge |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Geometric, control and numerical aspects of nonholonomic systems |c Jorge Cortés Monforte |
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London |b Springer |c 2002 | |
| 300 | |a XIV, 219 S. |b graph. Darst. | ||
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| 650 | 7 | |a Systeemtheorie |2 gtt | |
| 650 | 4 | |a Systèmes non holonomes | |
| 650 | 4 | |a Geometry, Differential | |
| 650 | 4 | |a Nonholonomic dynamical systems | |
| 650 | 4 | |a Nonlinear control theory | |
| 650 | 0 | 7 | |a Kontrolltheorie |0 (DE-588)4032317-1 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804129421846642688 |
|---|---|
| adam_text | Table of Contents
Preface VII
1 Introduction 1
1.1 Literature review 3
1.2 Contents 5
2 Basic geometric tools 13
2.1 Manifolds and tensor calculus 13
2.2 Generalized distributions and codistributions 17
2.3 Lie groups and group actions 18
2.4 Principal connections 23
2.5 Riemannian geometry 24
2.5.1 Metric connections 26
2.6 Symplectic manifolds 29
2.7 Symplectic and Hamiltonian actions 30
2.8 Almost Poisson manifolds 32
2.8.1 Almost Poisson reduction 33
2.9 The geometry of the tangent bundle 34
3 Nonholonomic systems 39
3.1 Variational principles in Mechanics 39
3.1.1 Hamilton s principle 39
3.1.2 Symplectic formulation 42
3.2 Introducing constraints 43
3.2.1 The rolling disk 45
3.2.2 A homogeneous ball on a rotating table 47
3.2.3 The Snakeboard 49
3.2.4 A variation of Benenti s example 50
3.3 The Lagrange d Alembert principle 51
X Table of Contents
3.4 Geometric formalizations 55
3.4.1 Symplectic approach 55
3.4.2 Affine connection approach 58
4 Symmetries of nonholonomic systems 63
4.1 Nonholonomic systems with symmetry 63
4.2 The purely kinematic case 67
4.2.1 Reduction 68
4.2.2 Reconstruction 77
4.3 The case of horizontal symmetries 80
4.3.1 Reduction 80
4.3.2 Reconstruction 81
4.4 The general case 84
4.4.1 Reduction 87
4.5 A special subcase: kinematic plus horizontal 98
4.5.1 The nonholonomic free particle modified 100
5 Chaplygin systems 103
5.1 Generalized Chaplygin systems 103
5.1.1 Reduction in the affine connection formalism 104
5.1.2 Reconstruction 107
5.2 Two motivating examples 107
5.2.1 Mobile robot with fixed orientation 107
5.2.2 Two wheeled planar mobile robot 109
5.3 Relation between both approaches 112
5.4 Invariant measure 114
5.4.1 Koiller s question 114
5.4.2 A counter example 119
6 A class of hybrid nonholonomic systems 121
6.1 Mechanical systems subject to constraints of variable rank ... 121
6.2 Impulsive forces 123
6.3 Generalized constraints 126
6.3.1 Momentum jumps 129
6.3.2 The holonomic case 134
6.4 Examples 134
6.4.1 The rolling sphere 135
6.4.2 Particle with constraint 138
Table of Contents XI
7 Nonholonomic integrators 141
7.1 Symplectic integration 142
7.2 Variational integrators 143
7.3 Discrete Lagrange d Alembert principle 145
7.4 Construction of integrators 148
7.5 Geometric invariance properties 153
7.5.1 The symplectic form 154
7.5.2 The momentum 154
7.5.3 Chaplygin systems 156
7.6 Numerical examples 166
7.6.1 Nonholonomic particle 166
7.6.2 Mobile robot with fixed orientation with a potential .. 168
8 Control of mechanical systems 171
8.1 Simple mechanical control systems 171
8.1.1 Homogeneity and Lie algebraic structure 173
8.1.2 Controllability notions 174
8.2 Existing results 175
8.2.1 On controllability 176
8.2.2 Series expansions 176
8.3 The one input case 178
8.4 Systems underactuated by one control 179
8.5 Examples 190
8.5.1 The planar rigid body 190
8.5.2 A simple example 191
8.6 Mechanical systems with isotropic damping 193
8.6.1 Local accessibility and controllability 194
8.6.2 Kinematic controllability 198
8.6.3 Series expansion 199
8.6.4 Systems underactuated by one control 202
References 203
Index 217
|
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| author | Cortés Monforte, Jorge |
| author_facet | Cortés Monforte, Jorge |
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| author_sort | Cortés Monforte, Jorge |
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| dewey-full | 510 516.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV014670704 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:04:53Z |
| institution | BVB |
| isbn | 3540441549 |
| language | English |
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| physical | XIV, 219 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Cortés Monforte, Jorge Verfasser aut Geometric, control and numerical aspects of nonholonomic systems Jorge Cortés Monforte Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London Springer 2002 XIV, 219 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1793 Commande non linéaire Controleleer gtt Géométrie différentielle Numerieke methoden gtt Systeemtheorie gtt Systèmes non holonomes Geometry, Differential Nonholonomic dynamical systems Nonlinear control theory Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Nichtholonome Bedingung (DE-588)4171735-1 gnd rswk-swf Mechanisches System (DE-588)4132811-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Nichtholonome Bedingung (DE-588)4171735-1 s Numerische Mathematik (DE-588)4042805-9 s DE-604 Kontrolltheorie (DE-588)4032317-1 s Differentialgeometrie (DE-588)4012248-7 s Mechanisches System (DE-588)4132811-5 s Lecture notes in mathematics 1793 (DE-604)BV000676446 1793 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009953245&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cortés Monforte, Jorge Geometric, control and numerical aspects of nonholonomic systems Lecture notes in mathematics Commande non linéaire Controleleer gtt Géométrie différentielle Numerieke methoden gtt Systeemtheorie gtt Systèmes non holonomes Geometry, Differential Nonholonomic dynamical systems Nonlinear control theory Kontrolltheorie (DE-588)4032317-1 gnd Differentialgeometrie (DE-588)4012248-7 gnd Numerische Mathematik (DE-588)4042805-9 gnd Dynamisches System (DE-588)4013396-5 gnd Nichtholonome Bedingung (DE-588)4171735-1 gnd Mechanisches System (DE-588)4132811-5 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4012248-7 (DE-588)4042805-9 (DE-588)4013396-5 (DE-588)4171735-1 (DE-588)4132811-5 |
| title | Geometric, control and numerical aspects of nonholonomic systems |
| title_auth | Geometric, control and numerical aspects of nonholonomic systems |
| title_exact_search | Geometric, control and numerical aspects of nonholonomic systems |
| title_full | Geometric, control and numerical aspects of nonholonomic systems Jorge Cortés Monforte |
| title_fullStr | Geometric, control and numerical aspects of nonholonomic systems Jorge Cortés Monforte |
| title_full_unstemmed | Geometric, control and numerical aspects of nonholonomic systems Jorge Cortés Monforte |
| title_short | Geometric, control and numerical aspects of nonholonomic systems |
| title_sort | geometric control and numerical aspects of nonholonomic systems |
| topic | Commande non linéaire Controleleer gtt Géométrie différentielle Numerieke methoden gtt Systeemtheorie gtt Systèmes non holonomes Geometry, Differential Nonholonomic dynamical systems Nonlinear control theory Kontrolltheorie (DE-588)4032317-1 gnd Differentialgeometrie (DE-588)4012248-7 gnd Numerische Mathematik (DE-588)4042805-9 gnd Dynamisches System (DE-588)4013396-5 gnd Nichtholonome Bedingung (DE-588)4171735-1 gnd Mechanisches System (DE-588)4132811-5 gnd |
| topic_facet | Commande non linéaire Controleleer Géométrie différentielle Numerieke methoden Systeemtheorie Systèmes non holonomes Geometry, Differential Nonholonomic dynamical systems Nonlinear control theory Kontrolltheorie Differentialgeometrie Numerische Mathematik Dynamisches System Nichtholonome Bedingung Mechanisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009953245&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT cortesmonfortejorge geometriccontrolandnumericalaspectsofnonholonomicsystems |