Geometric control of mechanical systems: modeling, analysis, and design for simple mechanical control systems
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2005
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| Series: | Texts in applied mathematics
49 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [657] - 688 |
| Physical Description: | XXIV, 726 S. graph. Darst. |
| ISBN: | 0387221956 |
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| 100 | 1 | |a Bullo, Francesco |e Verfasser |0 (DE-588)133913414 |4 aut | |
| 245 | 1 | 0 | |a Geometric control of mechanical systems |b modeling, analysis, and design for simple mechanical control systems |
| 264 | 1 | |a New York, NY |b Springer |c 2005 | |
| 300 | |a XXIV, 726 S. |b graph. Darst. | ||
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| 490 | 1 | |a Texts in applied mathematics |v 49 | |
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| adam_text | FRANCESCO BULLO ANDREW D. LEWIS GEOMETRIC CONTROL OF MECHANICAL SYSTEMS
MODELING, ANALYSIS, AND DESIGN FOR SIMPLE MECHANICAL CONTROL SYSTEMS
WITH 102 ILLUSTRATIONS §Y SPRINGER CONTENTS SERIES PREFACE VII PREFACE
IX PART I MODELING OF MECHANICAL SYSTEMS 1 INTRODUCTORY EXAMPLES AND
PROBLEMS 3 1.1 RIGID BODY SYSTEMS 4 1.2 MANIPULATORS AND MULTI-BODY
SYSTEMS 6 1.3 CONSTRAINED MECHANICAL SYSTEMS 8 1.4 BIBLIOGRAPHICAL NOTES
10 2 LINEAR AND MULTILINEAR ALGEBRA 15 2.1 BASIC CONCEPTS AND NOTATION
15 2.1.1 SETS AND SET NOTATION 16 2.1.2 NUMBER SYSTEMS AND THEIR
PROPERTIES 16 2.1.3 MAPS 17 2.1.4 RELATIONS 19 2.1.5 SEQUENCES AND
PERMUTATIONS 19 2.1.6 ZORN S LEMMA 20 2.2 VECTOR SPACES 21 2.2.1 BASIC
DEFINITIONS AND CONCEPTS 21 2.2.2 LINEAR MAPS 24 2.2.3 LINEAR MAPS AND
MATRICES 26 2.2.4 INVARIANT SUBSPACES, EIGENVALUES, AND EIGENVECTORS 29
2.2.5 DUAL SPACES 30 2.3 INNER PRODUCTS AND BILINEAR MAPS 33 2.3.1 INNER
PRODUCTS AND NORMS 33 2.3.2 LINEAR MAPS ON INNER PRODUCT SPACES 35 2.3.3
BILINEAR MAPS 36 XVIII CONTENTS 2.3.4 LINEAR MAPS ASSOCIATED WITH
BILINEAR MAPS 39 2.4 TENSORS 40 2.4.1 BASIC DEFINITIONS 41 2.4.2
REPRESENTATIONS OF TENSORS IN BASES 42 2.4.3 BEHAVIOR OF TENSORS UNDER
LINEAR MAPS 43 2.5 CONVEXITY 44 3 DIFFERENTIAL GEOMETRY 49 3.1 THE
PRELUDE TO DIFFERENTIAL GEOMETRY 50 3.1.1 TOPOLOGY 51 3.1.2 CALCULUS IN
R N 56 3.1.3 CONVERGENCE OF SEQUENCES OF MAPS 59 3.2 MANIFOLDS, MAPS,
AND SUBMANIFOLDS 60 3.2.1 CHARTS, ATLASES, AND DIFFERENTIABLE STRUCTURES
60 3.2.2 MAPS BETWEEN MANIFOLDS 66 3.2.3 SUBMANIFOLDS 68 3.3 TANGENT
BUNDLES AND MORE ABOUT MAPS 70 3.3.1 THE TANGENT BUNDLE 70 3.3.2 MORE
ABOUT MAPS 73 3.4 VECTOR BUNDLES 77 3.4.1 VECTOR BUNDLES 78 3.4.2 TENSOR
BUNDLES 83 3.5 VECTOR FIELDS 84 3.5.1 VECTOR FIELDS AS DIFFERENTIAL
OPERATORS 85 3.5.2 VECTOR FIELDS AND ORDINARY DIFFERENTIAL EQUATIONS 89
3.5.3 LIFTS OF VECTOR FIELDS TO THE TANGENT BUNDLE 94 3.6 TENSOR FIELDS
95 3.6.1 COVECTOR FIELDS 96 3.6.2 GENERAL TENSOR FIELDS 98 3.7
DISTRIBUTIONS AND CODISTRIBUTIONS 104 3.7.1 DEFINITIONS AND BASIC
PROPERTIES 104 3.7.2 INTEGRABLE DISTRIBUTIONS 105 3.7.3 THE ORBIT
THEOREM FOR DISTRIBUTIONS 108 3.7.4 CODISTRIBUTIONS 110 3.8 AFFINE
DIFFERENTIAL GEOMETRY ILL 3.8.1 DEFINITIONS AND GENERAL CONCEPTS 112
3.8.2 THE LEVI-CIVITA AFFINE CONNECTION 114 3.8.3 COORDINATE FORMULAE
116 3.8.4 THE SYMMETRIC PRODUCT 118 3.9 ADVANCED TOPICS IN
DIFFERENTIAL GEOMETRY 119 3.9.1 THE DIFFERENTIABLE STRUCTURE OF AN
IMMERSED SUBMANIFOLDL20 3.9.2 COMMENTS ON SMOOTHNESS, IN PARTICULAR
ANALYTICITY .... 121 3.9.3 PROPERTIES OF GENERALIZED SUBBUNDLES 123
3.9.4 AN ALTERNATIVE NOTION OF DISTRIBUTION ,125 3.9.5 FIBER BUNDLES 130
CONTENTS XIX 3.9.6 ADDITIONAL TOPICS IN AFFINE DIFFERENTIAL GEOMETRY 131
SIMPLE MECHANICAL CONTROL SYSTEMS 141 4.1 THE CONFIGURATION MANIFOLD 143
4.1.1 INTERCONNECTED MECHANICAL SYSTEMS 143 4.1.2 FINDING THE
CONFIGURATION MANIFOLD 146 4.1.3 CHOOSING COORDINATES 152 4.1.4 THE
FORWARD KINEMATIC MAP 155 4.1.5 THE TANGENT BUNDLE OF THE CONFIGURATION
MANIFOLD 157 4.2 THE KINETIC ENERGY METRIC 162 4.2.1 RIGID BODIES 162
4.2.2 THE KINETIC ENERGY OF A SINGLE RIGID BODY 166 4.2.3 FROM KINETIC
ENERGY TO A RIEMANNIAN METRIC 168 4.3 THE EULER-LAGRANGE EQUATIONS 172
4.3.1 A PROBLEM IN THE CALCULUS OF VARIATIONS 173 4.3.2 NECESSARY
CONDITIONS FOR MINIMIZATION*THE EULER-LAGRANGE EQUATIONS 174 4.3.3 THE
EULER-LAGRANGE EQUATIONS AND CHANGES OF COORDINATE 176 4.3.4 THE
EULER-LAGRANGE EQUATIONS ON A RIEMANNIAN MANIFOLD 178 4.3.5 PHYSICAL
INTERPRETATIONS 182 4.4 FORCES 187 4.4.1 FROM RIGID BODY FORCES AND
TORQUES TO LAGRANGIAN FORCES 188 4.4.2 DEFINITIONS AND EXAMPLES OF
FORCES IN LAGRANGIAN MECHANICS 189 4.4.3 THE LAGRANGE-D ALEMBERT
PRINCIPLE 193 4.4.4 POTENTIAL FORCES 195 4.4.5 DISSIPATIVE FORCES 198
4.5 NONHOLONOMIC CONSTRAINTS 198 4.5.1 FROM RIGID BODY CONSTRAINTS TO A
DISTRIBUTION ON Q .... 199 4.5.2 DEFINITIONS AND BASIC PROPERTIES 200
4.5.3 THE EULER-LAGRANGE EQUATIONS IN THE PRESENCE OF CONSTRAINTS 204
4.5.4 SIMPLE MECHANICAL SYSTEMS WITH CONSTRAINTS 207 4.5.5 THE
CONSTRAINED CONNECTION 209 4.5.6 THE POINCARE REPRESENTATION OF THE
EQUATIONS OF MOTION 213 4.5.7 SPECIAL FEATURES OF HOLONOINIC CONSTRAINTS
215 4.6 SIMPLE MECHANICAL CONTROL SYSTEMS AND THEIR REPRESENTATIONS ..
218 4.6.1 CONTROL-AFFINE SYSTEMS 218 4.6.2 CLASSES OF SIMPLE MECHANICAL
CONTROL SYSTEMS 221 4.6.3 GLOBAL REPRESENTATIONS OF EQUATIONS OF MOTION
224 4.6.4 LOCAL REPRESENTATIONS OF EQUATIONS OF MOTION 225 4.6.5 LINEAR
MECHANICAL CONTROL SYSTEMS 227 4.6.6 ALTERNATIVE FORMULATIONS 229
CONTENTS LIE GROUPS, SYSTEMS ON GROUPS, AND SYMMETRIES 247 5.1 RIGID
BODY KINEMATICS 248 5.1.1 RIGID BODY TRANSFORMATIONS 249 5.1.2
INFINITESIMAL RIGID BODY TRANSFORMATIONS 252 5.1.3 RIGID BODY
TRANSFORMATIONS AS EXPONENTIALS OF TWISTS . . . 254 5.1.4 COORDINATE
SYSTEMS ON THE GROUP OF RIGID DISPLACEMENTS 255 5.2 LIE GROUPS AND LIE
ALGEBRAS 258 5.2.1 GROUPS 258 5.2.2 FROM ONE-PARAMETER SUBGROUPS TO
MATRIX LIE ALGEBRAS . 261 5.2.3 LIE ALGEBRAS 263 5.2.4 THE LIE ALGEBRA
OF A LIE GROUP 265 5.2.5 THE LIE ALGEBRA OF A MATRIX LIE GROUP 268 5.3
METRICS, CONNECTIONS, AND SYSTEMS ON LIE GROUPS 271 5.3.1 INVARIANT
METRICS AND CONNECTIONS 271 5.3.2 SIMPLE MECHANICAL CONTROL SYSTEMS ON
LIE GROUPS 275 5.3.3 PLANAR AND THREE-DIMENSIONAL RIGID BODIES AS
SYSTEMS ON LIE GROUPS 277 5.4 GROUP ACTIONS, ISOMETRIES, AND SYMMETRIES
283 5.4.1 GROUP ACTIONS AND INFINITESIMAL GENERATORS 283 5.4.2
ISOMETRIES 288 5.4.3 SYMMETRIES AND CONSERVATION LAWS 290 5.4.4 EXAMPLES
OF MECHANICAL SYSTEMS WITH SYMMETRIES 293 5.5 PRINCIPAL BUNDLES AND
REDUCTION .. 296 5.5.1 PRINCIPAL FIBER BUNDLES 297 5.5.2 REDUCTION BY AN
INFINITESIMAL ISOMETRY 298 PART II ANALYSIS OF MECHANICAL CONTROL
SYSTEMS 6 STABILITY 313 6.1 AN OVERVIEW OF STABILITY THEORY FOR
DYNAMICAL SYSTEMS 315 6.1.1 STABILITY NOTIONS 315 6.1.2 LINEARIZATION
AND LINEAR STABILITY ANALYSIS 317 6.1.3 LYAPUNOV STABILITY CRITERIA AND
LASALLE INVARIANCE PRINCIPLE 319 6.1.4 ELEMENTS OF MORSE THEORY 325
6.1.5 EXPONENTIAL CONVERGENCE 327 6.1.6 QUADRATIC FUNCTIONS 329 6.2
STABILITY ANALYSIS FOR EQUILIBRIUM CONFIGURATIONS OF MECHANICAL SYSTEMS
331 6.2.1 LINEARIZATION OF SIMPLE MECHANICAL SYSTEMS 331 6.2.2 LINEAR
STABILITY ANALYSIS FOR UNFORCED SYSTEMS 334 6.2.3 LINEAR STABILITY
ANALYSIS FOR SYSTEMS SUBJECT TO RAYLEIGH DISSIPATION *336 6.2.4 LYAPUNOV
STABILITY ANALYSIS 340 CONTENTS XXI 6.2.5 GLOBAL STABILITY ANALYSIS 344
6.2.6 EXAMPLES ILLUSTRATING CONFIGURATION STABILITY RESULTS .... 345 6.3
RELATIVE EQUILIBRIA AND THEIR STABILITY 349 6.3.1 EXISTENCE AND
STABILITY DEFINITIONS 349 6.3.2 LYAPUNOV STABILITY ANALYSIS 351 6.3.3
EXAMPLES ILLUSTRATING EXISTENCE AND STABILITY OF RELATIVE EQUILIBRIA 355
6.3.4 RELATIVE EQUILIBRIA FOR SIMPLE MECHANICAL SYSTEMS ON LIE GROUPS
357 CONTROLLABILITY 367 7.1 AN OVERVIEW OF CONTROLLABILITY FOR
CONTROL-AFFINE SYSTEMS 368 7.1.1 REACHABLE SETS 369 7.1.2 NOTIONS OF
CONTROLLABILITY 371 7.1.3 THE SUSSMANN AND JURDJEVIC THEORY OF
ATTAINABILITY. . . . 372 7.1.4 FROM ATTAINABILITY TO ACCESSIBILITY 374
7.1.5 SOME RESULTS ON SMALL-TIME LOCAL CONTROLLABILITY 377 7.2
CONTROLLABILITY DEFINITIONS FOR MECHANICAL CONTROL SYSTEMS 387 7.3
CONTROLLABILITY RESULTS FOR MECHANICAL CONTROL SYSTEMS 389 7.3.1
LINEARIZATION RESULTS 390 7.3.2 ACCESSIBILITY OF AFFINE CONNECTION
CONTROL SYSTEMS 392 7.3.3 CONTROLLABILITY OF AFFINE CONNECTION CONTROL
SYSTEMS .... 394 7.4 EXAMPLES ILLUSTRATING CONTROLLABILITY RESULTS 398
7.4.1 ROBOTIC LEG 398 7.4.2 PLANAR BODY WITH VARIABLE-DIRECTION THRUSTER
400 7.4.3 ROLLING DISK 402 LOW-ORDER CONTROLLABILITY AND KINEMATIC
REDUCTION 411 8.1 VECTOR-VALUED QUADRATIC FORMS 412 8.1.1 BASIC
DEFINITIONS AND PROPERTIES 412 8.1.2 VECTOR-VALUED QUADRATIC FORMS AND
AFFINE CONNECTION CONTROL SYSTEMS 414 8.2 LOW-ORDER CONTROLLABILITY
RESULTS 415 8.2.1 CONSTRUCTIONS CONCERNING VANISHING INPUT VECTOR FIELDS
. 416 8.2.2 FIRST-ORDER CONTROLLABILITY RESULTS 417 8.2.3 EXAMPLES AND
DISCUSSION 420 8.3 REDUCTIONS OF AFFINE CONNECTION CONTROL SYSTEMS 422
8.3.1 INPUTS FOR DYNAMIC AND KINEMATIC SYSTEMS 422 8.3.2 KINEMATIC
REDUCTIONS 424 8.3.3 MAXIMALLY REDUCIBLE SYSTEMS 429 8.4 THE
RELATIONSHIP BETWEEN CONTROLLABILITY AND KINEMATIC CONTROLLABILITY 432
8.4.1 IMPLICATIONS 433 8.4.2 COUNTEREXAMPLES^ 434 XXII CONTENTS 9
PERTURBATION ANALYSIS 441 9.1 AN OVERVIEW OF AVERAGING THEORY FOR
OSCILLATORY CONTROL SYSTEMS 442 9.1.1 ITERATED INTEGRALS AND THEIR
AVERAGES 443 9.1.2 NORMS FOR OBJECTS DEFINED ON COMPLEX NEIGHBORHOODS ..
446 9.1.3 THE VARIATION OF CONSTANTS FORMULA 447 9.1.4 FIRST-ORDER
AVERAGING 451 9.1.5 AVERAGING OF SYSTEMS SUBJECT TO OSCILLATORY INPUTS
454 9.1.6 SERIES EXPANSION RESULTS FOR AVERAGING 459 9.2 AVERAGING OF
AFFINE CONNECTION SYSTEMS SUBJECT TO OSCILLATORY CONTROLS 463 9.2.1 THE
HOMOGENEITY PROPERTIES OF AFFINE CONNECTION CONTROL SYSTEMS 463 9.2.2
FLOWS FOR HOMOGENEOUS VECTOR FIELDS 466 9.2.3 AVERAGING ANALYSIS 466
9.2.4 SIMPLE MECHANICAL CONTROL SYSTEMS WITH POTENTIAL CONTROL FORCES
471 9.3 A SERIES EXPANSION FOR A CONTROLLED TRAJECTORY FROM REST 473
PART III A SAMPLING OF DESIGN METHODOLOGIES 10 LINEAR AND NONLINEAR
POTENTIAL SHAPING FOR STABILIZATION .... 481 10.1 AN OVERVIEW OF
STABILIZATION 482 10.1.1 DEFINING THE PROBLEM 483 10.1.2 STABILIZATION
USING LINEARIZATION 485 10.1.3 THE GAPS IN LINEAR STABILIZATION THEORY
487 10.1.4 CONTROL-LYAPUNOV FUNCTIONS 489 10.1.5 LYAPUNOV-BASED
DISSIPATIVE CONTROL 490 10.2 STABILIZATION PROBLEMS FOR MECHANICAL
SYSTEMS 493 10.3 STABILIZATION USING LINEAR POTENTIAL SHAPING 495 10.3.1
LINEAR PD CONTROL 495 10.3.2 STABILIZATION USING LINEAR PD CONTROL 497
10.3.3 IMPLEMENTING LINEAR CONTROL LAWS ON NONLINEAR SYSTEMS . 501
10.3.4 APPLICATION TO THE TWO-LINK MANIPULATOR 505 10.4 STABILIZATION
USING NONLINEAR POTENTIAL SHAPING 507 10.4.1 NONLINEAR PD CONTROL AND
POTENTIAL ENERGY SHAPING .... 507 10.4.2 STABILIZATION USING NONLINEAR
PD CONTROL 509 10.4.3 A MATHEMATICAL EXAMPLE 515 10.5 NOTES ON
STABILIZATION OF MECHANICAL SYSTEMS 515 10.5.1 GENERAL LINEAR TECHNIQUES
516 10.5.2 FEEDBACK LINEARIZATION AND PARTIAL FEEDBACK LINEARIZATION517
10.5.3 BACKSTEPPING 517 10.5.4 PASSIVITY-BASED METHODS 518 10.5.5
SLIDING MODE CONTROL % 518 10.5.6 TOTAL ENERGY SHAPING METHODS 519
CONTENTS XXIII 10.5.7 WHEN STABILIZATION BY SMOOTH FEEDBACK IS NOT
POSSIBLE . 520 11 STABILIZATION AND TRACKING FOR FULLY ACTUATED SYSTEMS
529 11.1 CONFIGURATION STABILIZATION FOR FULLY ACTUATED SYSTEMS 530
11.1.1 STABILIZATION VIA CONFIGURATION ERROR FUNCTIONS 530 11.1.2 PD
CONTROL FOR A POINT MASS IN THREE-DIMENSIONAL EUCLIDEAN SPACE 532 11.1.3
PD CONTROL FOR THE SPHERICAL PENDULUM 533 I 11.2 TRAJECTORY TRACKING FOR
FULLY ACTUATED SYSTEMS 534 F 11.2.1 TIME-DEPENDENT FEEDBACK CONTROL AND
THE TRACKING [ PROBLEM 534 ! _ 11.2.2 TRACKING ERROR FUNCTIONS 535 *
11.2.3 TRANSPORT MAPS 536 I, 11.2.4 VELOCITY ERROR CURVES 538 5 11.2.5
PROPORTIONAL-DERIVATIVE AND FEEDFORWARD CONTROL 540 I 11.3 EXAMPLES
ILLUSTRATING TRAJECTORY TRACKING RESULTS 542 11.3.1 PD AND FEEDFORWARD
CONTROL FOR A POINT MASS IN THREE-DIMENSIONAL EUCLIDEAN SPACE 542 11.3.2
PD AND FEEDFORWARD CONTROL FOR THE SPHERICAL PENDULUM 543 11.4
STABILIZATION AND TRACKING ON LIE GROUPS 546 11.4.1 PD CONTROL ON LIE
GROUPS 547 11.4.2 PD AND FEEDFORWARD CONTROL ON LIE GROUPS 548 11.4.3
THE ATTITUDE TRACKING PROBLEM FOR A FULLY ACTUATED RIGID BODY FIXED AT A
POINT 552 12 STABILIZATION AND TRACKING USING OSCILLATORY CONTROLS 559
12.1 THE DESIGN OF OSCILLATORY CONTROLS 560 12.1.1 THE AVERAGING
OPERATOR 560 12.1.2 INVERTING THE AVERAGING OPERATOR 563 12.2
STABILIZATION VIA OSCILLATORY CONTROLS 567 12.2.1 STABILIZATION WITH THE
CONTROLLABILITY ASSUMPTION 568 12.2.2 STABILIZATION WITHOUT THE
CONTROLLABILITY ASSUMPTION.... 571 12.3 TRACKING VIA OSCILLATORY
CONTROLS 574 13 MOTION PLANNING FOR UNDERACTUATED SYSTEMS 583 13.1
MOTION PLANNING FOR DRIFTLESS SYSTEMS 584 13.1.1 DEFINITIONS 584 13.1.2
A BRIEF LITERATURE SURVEY OF SYNTHESIS METHODS 587 13.2 MOTION PLANNING
FOR MECHANICAL SYSTEMS 589 13.2.1 DEFINITIONS 589 13.2.2 KINEMATICALLY
CONTROLLABLE SYSTEMS 590 13.2.3 MAXIMALLY REDUCIBLE SYSTEMS 591 13.3
MOTION PLANNING FOR TWO SIMPLE SYSTEMS 593 13.3.1 MOTION PLANNING FOR
THE PLANAR RIGID BODY 593 13.3.2 MOTION PLANNING TOR THE ROBOTIC LEG 596
XXIV CONTENTS 13.4 MOTION PLANNING FOR THE SNAKEBOARD 598 13.4.1
MODELING 598 13.4.2 MOTION PLANNING ON SE(2) FOR THE SNAKEBOARD 605
13.4.3 SIMULATIONS 612 A TIME-DEPENDENT VECTOR FIELDS 619 A.I MEASURE
AND INTEGRATION 619 A.1.1 GENERAL MEASURE THEORY 619 A.I.2 LEBESGUE
MEASURE 621 A.I.3 LEBESGUE INTEGRATION 622 A.2 VECTOR FIELDS WITH
MEASURABLE TIME-DEPENDENCE 624 A.2.1 CARATHEODORY SECTIONS OF VECTOR
BUNDLES AND BUNDLE MAPS 624 A.2.2 THE TIME-DEPENDENT FLOW BOX THEOREM
625 B SOME PROOFS 627 B.I PROOF OF THEOREM 4.38 627 B.2 PROOF OF THEOREM
7.36 629 B.3 PROOF OF LEMMA 8.4 635 B.4 PROOF OF THEOREM 9.38 638 B.5
PROOF OF THEOREM 11.19 648 B.6 PROOF OF THEOREM 11.29 652 B.7 PROOF OF
PROPOSITION 12.9 654 REFERENCES 65 7 SYMBOL INDEX 689 SUBJECT INDEX 705
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| adam_txt |
FRANCESCO BULLO ANDREW D. LEWIS GEOMETRIC CONTROL OF MECHANICAL SYSTEMS
MODELING, ANALYSIS, AND DESIGN FOR SIMPLE MECHANICAL CONTROL SYSTEMS
WITH 102 ILLUSTRATIONS §Y SPRINGER CONTENTS SERIES PREFACE VII PREFACE
IX PART I MODELING OF MECHANICAL SYSTEMS 1 INTRODUCTORY EXAMPLES AND
PROBLEMS 3 1.1 RIGID BODY SYSTEMS 4 1.2 MANIPULATORS AND MULTI-BODY
SYSTEMS 6 1.3 CONSTRAINED MECHANICAL SYSTEMS 8 1.4 BIBLIOGRAPHICAL NOTES
10 2 LINEAR AND MULTILINEAR ALGEBRA 15 2.1 BASIC CONCEPTS AND NOTATION
15 2.1.1 SETS AND SET NOTATION 16 2.1.2 NUMBER SYSTEMS AND THEIR
PROPERTIES 16 2.1.3 MAPS 17 2.1.4 RELATIONS 19 2.1.5 SEQUENCES AND
PERMUTATIONS 19 2.1.6 ZORN'S LEMMA 20 2.2 VECTOR SPACES 21 2.2.1 BASIC
DEFINITIONS AND CONCEPTS 21 2.2.2 LINEAR MAPS 24 2.2.3 LINEAR MAPS AND
MATRICES 26 2.2.4 INVARIANT SUBSPACES, EIGENVALUES, AND EIGENVECTORS 29
2.2.5 DUAL SPACES 30 2.3 INNER PRODUCTS AND BILINEAR MAPS 33 2.3.1 INNER
PRODUCTS AND NORMS 33 2.3.2 LINEAR MAPS ON INNER PRODUCT SPACES 35 2.3.3
BILINEAR MAPS 36 XVIII CONTENTS 2.3.4 LINEAR MAPS ASSOCIATED WITH
BILINEAR MAPS 39 2.4 TENSORS 40 2.4.1 BASIC DEFINITIONS 41 2.4.2
REPRESENTATIONS OF TENSORS IN BASES 42 2.4.3 BEHAVIOR OF TENSORS UNDER
LINEAR MAPS 43 2.5 CONVEXITY 44 3 DIFFERENTIAL GEOMETRY 49 3.1 THE
PRELUDE TO DIFFERENTIAL GEOMETRY 50 3.1.1 TOPOLOGY 51 3.1.2 CALCULUS IN
R N 56 3.1.3 CONVERGENCE OF SEQUENCES OF MAPS 59 3.2 MANIFOLDS, MAPS,
AND SUBMANIFOLDS 60 3.2.1 CHARTS, ATLASES, AND DIFFERENTIABLE STRUCTURES
60 3.2.2 MAPS BETWEEN MANIFOLDS 66 3.2.3 SUBMANIFOLDS 68 3.3 TANGENT
BUNDLES AND MORE ABOUT MAPS 70 3.3.1 THE TANGENT BUNDLE 70 3.3.2 MORE
ABOUT MAPS 73 3.4 VECTOR BUNDLES 77 3.4.1 VECTOR BUNDLES 78 3.4.2 TENSOR
BUNDLES 83 3.5 VECTOR FIELDS 84 3.5.1 VECTOR FIELDS AS DIFFERENTIAL
OPERATORS 85 3.5.2 VECTOR FIELDS AND ORDINARY DIFFERENTIAL EQUATIONS 89
3.5.3 LIFTS OF VECTOR FIELDS TO THE TANGENT BUNDLE 94 3.6 TENSOR FIELDS
95 3.6.1 COVECTOR FIELDS 96 3.6.2 GENERAL TENSOR FIELDS 98 3.7
DISTRIBUTIONS AND CODISTRIBUTIONS 104 3.7.1 DEFINITIONS AND BASIC
PROPERTIES 104 3.7.2 INTEGRABLE DISTRIBUTIONS 105 3.7.3 THE ORBIT
THEOREM FOR DISTRIBUTIONS 108 3.7.4 CODISTRIBUTIONS 110 3.8 AFFINE
DIFFERENTIAL GEOMETRY ILL 3.8.1 DEFINITIONS AND GENERAL CONCEPTS 112
3.8.2 THE LEVI-CIVITA AFFINE CONNECTION 114 3.8.3 COORDINATE FORMULAE
116 3.8.4 THE SYMMETRIC PRODUCT 118 3.9 ADVANCED TOPICS IN
DIFFERENTIAL GEOMETRY 119 3.9.1 THE DIFFERENTIABLE STRUCTURE OF AN
IMMERSED SUBMANIFOLDL20 3.9.2 COMMENTS ON SMOOTHNESS, IN PARTICULAR
ANALYTICITY . 121 3.9.3 PROPERTIES OF GENERALIZED SUBBUNDLES 123
3.9.4 AN ALTERNATIVE NOTION OF DISTRIBUTION ,125 3.9.5 FIBER BUNDLES 130
CONTENTS XIX 3.9.6 ADDITIONAL TOPICS IN AFFINE DIFFERENTIAL GEOMETRY 131
SIMPLE MECHANICAL CONTROL SYSTEMS 141 4.1 THE CONFIGURATION MANIFOLD 143
4.1.1 INTERCONNECTED MECHANICAL SYSTEMS 143 4.1.2 FINDING THE
CONFIGURATION MANIFOLD 146 4.1.3 CHOOSING COORDINATES 152 4.1.4 THE
FORWARD KINEMATIC MAP 155 4.1.5 THE TANGENT BUNDLE OF THE CONFIGURATION
MANIFOLD 157 4.2 THE KINETIC ENERGY METRIC 162 4.2.1 RIGID BODIES 162
4.2.2 THE KINETIC ENERGY OF A SINGLE RIGID BODY 166 4.2.3 FROM KINETIC
ENERGY TO A RIEMANNIAN METRIC 168 4.3 THE EULER-LAGRANGE EQUATIONS 172
4.3.1 A PROBLEM IN THE CALCULUS OF VARIATIONS 173 4.3.2 NECESSARY
CONDITIONS FOR MINIMIZATION*THE EULER-LAGRANGE EQUATIONS 174 4.3.3 THE
EULER-LAGRANGE EQUATIONS AND CHANGES OF COORDINATE 176 4.3.4 THE
EULER-LAGRANGE EQUATIONS ON A RIEMANNIAN MANIFOLD 178 4.3.5 PHYSICAL
INTERPRETATIONS 182 4.4 FORCES 187 4.4.1 FROM RIGID BODY FORCES AND
TORQUES TO LAGRANGIAN FORCES 188 4.4.2 DEFINITIONS AND EXAMPLES OF
FORCES IN LAGRANGIAN MECHANICS 189 4.4.3 THE LAGRANGE-D'ALEMBERT
PRINCIPLE 193 4.4.4 POTENTIAL FORCES 195 4.4.5 DISSIPATIVE FORCES 198
4.5 NONHOLONOMIC CONSTRAINTS 198 4.5.1 FROM RIGID BODY CONSTRAINTS TO A
DISTRIBUTION ON Q . 199 4.5.2 DEFINITIONS AND BASIC PROPERTIES 200
4.5.3 THE EULER-LAGRANGE EQUATIONS IN THE PRESENCE OF CONSTRAINTS 204
4.5.4 SIMPLE MECHANICAL SYSTEMS WITH CONSTRAINTS 207 4.5.5 THE
CONSTRAINED CONNECTION 209 4.5.6 THE POINCARE REPRESENTATION OF THE
EQUATIONS OF MOTION 213 4.5.7 SPECIAL FEATURES OF HOLONOINIC CONSTRAINTS
215 4.6 SIMPLE MECHANICAL CONTROL SYSTEMS AND THEIR REPRESENTATIONS .
218 4.6.1 CONTROL-AFFINE SYSTEMS 218 4.6.2 CLASSES OF SIMPLE MECHANICAL
CONTROL SYSTEMS 221 4.6.3 GLOBAL REPRESENTATIONS OF EQUATIONS OF MOTION
224 4.6.4 LOCAL REPRESENTATIONS OF EQUATIONS OF MOTION 225 4.6.5 LINEAR
MECHANICAL CONTROL SYSTEMS 227 4.6.6 ALTERNATIVE FORMULATIONS 229
CONTENTS LIE GROUPS, SYSTEMS ON GROUPS, AND SYMMETRIES 247 5.1 RIGID
BODY KINEMATICS 248 5.1.1 RIGID BODY TRANSFORMATIONS 249 5.1.2
INFINITESIMAL RIGID BODY TRANSFORMATIONS 252 5.1.3 RIGID BODY
TRANSFORMATIONS AS EXPONENTIALS OF TWISTS . . . 254 5.1.4 COORDINATE
SYSTEMS ON THE GROUP OF RIGID DISPLACEMENTS 255 5.2 LIE GROUPS AND LIE
ALGEBRAS 258 5.2.1 GROUPS 258 5.2.2 FROM ONE-PARAMETER SUBGROUPS TO
MATRIX LIE ALGEBRAS . 261 5.2.3 LIE ALGEBRAS 263 5.2.4 THE LIE ALGEBRA
OF A LIE GROUP 265 5.2.5 THE LIE ALGEBRA OF A MATRIX LIE GROUP 268 5.3
METRICS, CONNECTIONS, AND SYSTEMS ON LIE GROUPS 271 5.3.1 INVARIANT
METRICS AND CONNECTIONS 271 5.3.2 SIMPLE MECHANICAL CONTROL SYSTEMS ON
LIE GROUPS 275 5.3.3 PLANAR AND THREE-DIMENSIONAL RIGID BODIES AS
SYSTEMS ON LIE GROUPS 277 5.4 GROUP ACTIONS, ISOMETRIES, AND SYMMETRIES
283 5.4.1 GROUP ACTIONS AND INFINITESIMAL GENERATORS 283 5.4.2
ISOMETRIES 288 5.4.3 SYMMETRIES AND CONSERVATION LAWS 290 5.4.4 EXAMPLES
OF MECHANICAL SYSTEMS WITH SYMMETRIES 293 5.5 PRINCIPAL BUNDLES AND
REDUCTION . 296 5.5.1 PRINCIPAL FIBER BUNDLES 297 5.5.2 REDUCTION BY AN
INFINITESIMAL ISOMETRY 298 PART II ANALYSIS OF MECHANICAL CONTROL
SYSTEMS 6 STABILITY 313 6.1 AN OVERVIEW OF STABILITY THEORY FOR
DYNAMICAL SYSTEMS 315 6.1.1 STABILITY NOTIONS 315 6.1.2 LINEARIZATION
AND LINEAR STABILITY ANALYSIS 317 6.1.3 LYAPUNOV STABILITY CRITERIA AND
LASALLE INVARIANCE PRINCIPLE 319 6.1.4 ELEMENTS OF MORSE THEORY 325
6.1.5 EXPONENTIAL CONVERGENCE 327 6.1.6 QUADRATIC FUNCTIONS 329 6.2
STABILITY ANALYSIS FOR EQUILIBRIUM CONFIGURATIONS OF MECHANICAL SYSTEMS
331 6.2.1 LINEARIZATION OF SIMPLE MECHANICAL SYSTEMS 331 6.2.2 LINEAR
STABILITY ANALYSIS FOR UNFORCED SYSTEMS 334 6.2.3 LINEAR STABILITY
ANALYSIS FOR SYSTEMS SUBJECT TO RAYLEIGH DISSIPATION *336 6.2.4 LYAPUNOV
STABILITY ANALYSIS 340 CONTENTS XXI 6.2.5 GLOBAL STABILITY ANALYSIS 344
6.2.6 EXAMPLES ILLUSTRATING CONFIGURATION STABILITY RESULTS . 345 6.3
RELATIVE EQUILIBRIA AND THEIR STABILITY 349 6.3.1 EXISTENCE AND
STABILITY DEFINITIONS 349 6.3.2 LYAPUNOV STABILITY ANALYSIS 351 6.3.3
EXAMPLES ILLUSTRATING EXISTENCE AND STABILITY OF RELATIVE EQUILIBRIA 355
6.3.4 RELATIVE EQUILIBRIA FOR SIMPLE MECHANICAL SYSTEMS ON LIE GROUPS
357 CONTROLLABILITY 367 7.1 AN OVERVIEW OF CONTROLLABILITY FOR
CONTROL-AFFINE SYSTEMS 368 7.1.1 REACHABLE SETS 369 7.1.2 NOTIONS OF
CONTROLLABILITY 371 7.1.3 THE SUSSMANN AND JURDJEVIC THEORY OF
ATTAINABILITY. . . . 372 7.1.4 FROM ATTAINABILITY TO ACCESSIBILITY 374
7.1.5 SOME RESULTS ON SMALL-TIME LOCAL CONTROLLABILITY 377 7.2
CONTROLLABILITY DEFINITIONS FOR MECHANICAL CONTROL SYSTEMS 387 7.3
CONTROLLABILITY RESULTS FOR MECHANICAL CONTROL SYSTEMS 389 7.3.1
LINEARIZATION RESULTS 390 7.3.2 ACCESSIBILITY OF AFFINE CONNECTION
CONTROL SYSTEMS 392 7.3.3 CONTROLLABILITY OF AFFINE CONNECTION CONTROL
SYSTEMS . 394 7.4 EXAMPLES ILLUSTRATING CONTROLLABILITY RESULTS 398
7.4.1 ROBOTIC LEG 398 7.4.2 PLANAR BODY WITH VARIABLE-DIRECTION THRUSTER
400 7.4.3 ROLLING DISK 402 LOW-ORDER CONTROLLABILITY AND KINEMATIC
REDUCTION 411 8.1 VECTOR-VALUED QUADRATIC FORMS 412 8.1.1 BASIC
DEFINITIONS AND PROPERTIES 412 8.1.2 VECTOR-VALUED QUADRATIC FORMS AND
AFFINE CONNECTION CONTROL SYSTEMS 414 8.2 LOW-ORDER CONTROLLABILITY
RESULTS 415 8.2.1 CONSTRUCTIONS CONCERNING VANISHING INPUT VECTOR FIELDS
. 416 8.2.2 FIRST-ORDER CONTROLLABILITY RESULTS 417 8.2.3 EXAMPLES AND
DISCUSSION 420 8.3 REDUCTIONS OF AFFINE CONNECTION CONTROL SYSTEMS 422
8.3.1 INPUTS FOR DYNAMIC AND KINEMATIC SYSTEMS 422 8.3.2 KINEMATIC
REDUCTIONS 424 8.3.3 MAXIMALLY REDUCIBLE SYSTEMS 429 8.4 THE
RELATIONSHIP BETWEEN CONTROLLABILITY AND KINEMATIC CONTROLLABILITY 432
8.4.1 IMPLICATIONS 433 8.4.2 COUNTEREXAMPLES^ 434 XXII CONTENTS 9
PERTURBATION ANALYSIS 441 9.1 AN OVERVIEW OF AVERAGING THEORY FOR
OSCILLATORY CONTROL SYSTEMS 442 9.1.1 ITERATED INTEGRALS AND THEIR
AVERAGES 443 9.1.2 NORMS FOR OBJECTS DEFINED ON COMPLEX NEIGHBORHOODS .
446 9.1.3 THE VARIATION OF CONSTANTS FORMULA 447 9.1.4 FIRST-ORDER
AVERAGING 451 9.1.5 AVERAGING OF SYSTEMS SUBJECT TO OSCILLATORY INPUTS
454 9.1.6 SERIES EXPANSION RESULTS FOR AVERAGING 459 9.2 AVERAGING OF
AFFINE CONNECTION SYSTEMS SUBJECT TO OSCILLATORY CONTROLS 463 9.2.1 THE
HOMOGENEITY PROPERTIES OF AFFINE CONNECTION CONTROL SYSTEMS 463 9.2.2
FLOWS FOR HOMOGENEOUS VECTOR FIELDS 466 9.2.3 AVERAGING ANALYSIS 466
9.2.4 SIMPLE MECHANICAL CONTROL SYSTEMS WITH POTENTIAL CONTROL FORCES
471 9.3 A SERIES EXPANSION FOR A CONTROLLED TRAJECTORY FROM REST 473
PART III A SAMPLING OF DESIGN METHODOLOGIES 10 LINEAR AND NONLINEAR
POTENTIAL SHAPING FOR STABILIZATION . 481 10.1 AN OVERVIEW OF
STABILIZATION 482 10.1.1 DEFINING THE PROBLEM 483 10.1.2 STABILIZATION
USING LINEARIZATION 485 10.1.3 THE GAPS IN LINEAR STABILIZATION THEORY
487 10.1.4 CONTROL-LYAPUNOV FUNCTIONS 489 10.1.5 LYAPUNOV-BASED
DISSIPATIVE CONTROL 490 10.2 STABILIZATION PROBLEMS FOR MECHANICAL
SYSTEMS 493 10.3 STABILIZATION USING LINEAR POTENTIAL SHAPING 495 10.3.1
LINEAR PD CONTROL 495 10.3.2 STABILIZATION USING LINEAR PD CONTROL 497
10.3.3 IMPLEMENTING LINEAR CONTROL LAWS ON NONLINEAR SYSTEMS . 501
10.3.4 APPLICATION TO THE TWO-LINK MANIPULATOR 505 10.4 STABILIZATION
USING NONLINEAR POTENTIAL SHAPING 507 10.4.1 NONLINEAR PD CONTROL AND
POTENTIAL ENERGY SHAPING . 507 10.4.2 STABILIZATION USING NONLINEAR
PD CONTROL 509 10.4.3 A MATHEMATICAL EXAMPLE 515 10.5 NOTES ON
STABILIZATION OF MECHANICAL SYSTEMS 515 10.5.1 GENERAL LINEAR TECHNIQUES
516 10.5.2 FEEDBACK LINEARIZATION AND PARTIAL FEEDBACK LINEARIZATION517
10.5.3 BACKSTEPPING 517 10.5.4 PASSIVITY-BASED METHODS 518 10.5.5
SLIDING MODE CONTROL % 518 10.5.6 TOTAL ENERGY SHAPING METHODS 519
CONTENTS XXIII 10.5.7 WHEN STABILIZATION BY SMOOTH FEEDBACK IS NOT
POSSIBLE . 520 11 STABILIZATION AND TRACKING FOR FULLY ACTUATED SYSTEMS
529 11.1 CONFIGURATION STABILIZATION FOR FULLY ACTUATED SYSTEMS 530
11.1.1 STABILIZATION VIA CONFIGURATION ERROR FUNCTIONS 530 11.1.2 PD
CONTROL FOR A POINT MASS IN THREE-DIMENSIONAL EUCLIDEAN SPACE 532 11.1.3
PD CONTROL FOR THE SPHERICAL PENDULUM 533 I 11.2 TRAJECTORY TRACKING FOR
FULLY ACTUATED SYSTEMS 534 F 11.2.1 TIME-DEPENDENT FEEDBACK CONTROL AND
THE TRACKING [ PROBLEM 534 ! _ 11.2.2 TRACKING ERROR FUNCTIONS 535 *
11.2.3 TRANSPORT MAPS 536 I, 11.2.4 VELOCITY ERROR CURVES 538 5 11.2.5
PROPORTIONAL-DERIVATIVE AND FEEDFORWARD CONTROL 540 I 11.3 EXAMPLES
ILLUSTRATING TRAJECTORY TRACKING RESULTS 542 11.3.1 PD AND FEEDFORWARD
CONTROL FOR A POINT MASS IN THREE-DIMENSIONAL EUCLIDEAN SPACE 542 11.3.2
PD AND FEEDFORWARD CONTROL FOR THE SPHERICAL PENDULUM 543 11.4
STABILIZATION AND TRACKING ON LIE GROUPS 546 11.4.1 PD CONTROL ON LIE
GROUPS 547 11.4.2 PD AND FEEDFORWARD CONTROL ON LIE GROUPS 548 11.4.3
THE ATTITUDE TRACKING PROBLEM FOR A FULLY ACTUATED RIGID BODY FIXED AT A
POINT 552 12 STABILIZATION AND TRACKING USING OSCILLATORY CONTROLS 559
12.1 THE DESIGN OF OSCILLATORY CONTROLS 560 12.1.1 THE AVERAGING
OPERATOR 560 12.1.2 INVERTING THE AVERAGING OPERATOR 563 12.2
STABILIZATION VIA OSCILLATORY CONTROLS 567 12.2.1 STABILIZATION WITH THE
CONTROLLABILITY ASSUMPTION 568 12.2.2 STABILIZATION WITHOUT THE
CONTROLLABILITY ASSUMPTION. 571 12.3 TRACKING VIA OSCILLATORY
CONTROLS 574 13 MOTION PLANNING FOR UNDERACTUATED SYSTEMS 583 13.1
MOTION PLANNING FOR DRIFTLESS SYSTEMS 584 13.1.1 DEFINITIONS 584 13.1.2
A BRIEF LITERATURE SURVEY OF SYNTHESIS METHODS 587 13.2 MOTION PLANNING
FOR MECHANICAL SYSTEMS 589 13.2.1 DEFINITIONS 589 13.2.2 KINEMATICALLY
CONTROLLABLE SYSTEMS 590 13.2.3 MAXIMALLY REDUCIBLE SYSTEMS 591 13.3
MOTION PLANNING FOR TWO SIMPLE SYSTEMS 593 13.3.1 MOTION PLANNING FOR
THE PLANAR RIGID BODY 593 13.3.2 MOTION PLANNING TOR THE ROBOTIC LEG 596
XXIV CONTENTS 13.4 MOTION PLANNING FOR THE SNAKEBOARD 598 13.4.1
MODELING 598 13.4.2 MOTION PLANNING ON SE(2) FOR THE SNAKEBOARD 605
13.4.3 SIMULATIONS 612 A TIME-DEPENDENT VECTOR FIELDS 619 A.I MEASURE
AND INTEGRATION 619 A.1.1 GENERAL MEASURE THEORY 619 A.I.2 LEBESGUE
MEASURE 621 A.I.3 LEBESGUE INTEGRATION 622 A.2 VECTOR FIELDS WITH
MEASURABLE TIME-DEPENDENCE 624 A.2.1 CARATHEODORY SECTIONS OF VECTOR
BUNDLES AND BUNDLE MAPS 624 A.2.2 THE TIME-DEPENDENT FLOW BOX THEOREM
625 B SOME PROOFS 627 B.I PROOF OF THEOREM 4.38 627 B.2 PROOF OF THEOREM
7.36 629 B.3 PROOF OF LEMMA 8.4 635 B.4 PROOF OF THEOREM 9.38 638 B.5
PROOF OF THEOREM 11.19 648 B.6 PROOF OF THEOREM 11.29 652 B.7 PROOF OF
PROPOSITION 12.9 654 REFERENCES 65 7 SYMBOL INDEX 689 SUBJECT INDEX 705 |
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| author | Bullo, Francesco Lewis, Andrew D. |
| author_GND | (DE-588)133913414 |
| author_facet | Bullo, Francesco Lewis, Andrew D. |
| author_role | aut aut |
| author_sort | Bullo, Francesco |
| author_variant | f b fb a d l ad adl |
| building | Verbundindex |
| bvnumber | BV022143704 |
| callnumber-first | T - Technology |
| callnumber-label | TJ213 |
| callnumber-raw | TJ213 |
| callnumber-search | TJ213 |
| callnumber-sort | TJ 3213 |
| callnumber-subject | TJ - Mechanical Engineering and Machinery |
| classification_rvk | SK 880 SK 950 |
| ctrlnum | (OCoLC)55682529 (DE-599)BVBBV022143704 |
| dewey-full | 629.8 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 629 - Other branches of engineering |
| dewey-raw | 629.8 |
| dewey-search | 629.8 |
| dewey-sort | 3629.8 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| discipline_str_mv | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| format | Book |
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| illustrated | Illustrated |
| index_date | 2024-07-02T16:17:45Z |
| indexdate | 2024-07-09T20:51:18Z |
| institution | BVB |
| isbn | 0387221956 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015358332 |
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| spelling | Bullo, Francesco Verfasser (DE-588)133913414 aut Geometric control of mechanical systems modeling, analysis, and design for simple mechanical control systems New York, NY Springer 2005 XXIV, 726 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 49 Literaturverz. S. [657] - 688 Commande automatique Controle automático larpcal Física matemática larpcal Geometria diferencial larpcal Géométrie différentielle Automatic control Geometry, Differential Mechanisches System (DE-588)4132811-5 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 s Mechanisches System (DE-588)4132811-5 s DE-604 Lewis, Andrew D. Verfasser aut Texts in applied mathematics 49 (DE-604)BV002476038 49 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015358332&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bullo, Francesco Lewis, Andrew D. Geometric control of mechanical systems modeling, analysis, and design for simple mechanical control systems Texts in applied mathematics Commande automatique Controle automático larpcal Física matemática larpcal Geometria diferencial larpcal Géométrie différentielle Automatic control Geometry, Differential Mechanisches System (DE-588)4132811-5 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
| subject_GND | (DE-588)4132811-5 (DE-588)4032317-1 |
| title | Geometric control of mechanical systems modeling, analysis, and design for simple mechanical control systems |
| title_auth | Geometric control of mechanical systems modeling, analysis, and design for simple mechanical control systems |
| title_exact_search | Geometric control of mechanical systems modeling, analysis, and design for simple mechanical control systems |
| title_exact_search_txtP | Geometric control of mechanical systems modeling, analysis, and design for simple mechanical control systems |
| title_full | Geometric control of mechanical systems modeling, analysis, and design for simple mechanical control systems |
| title_fullStr | Geometric control of mechanical systems modeling, analysis, and design for simple mechanical control systems |
| title_full_unstemmed | Geometric control of mechanical systems modeling, analysis, and design for simple mechanical control systems |
| title_short | Geometric control of mechanical systems |
| title_sort | geometric control of mechanical systems modeling analysis and design for simple mechanical control systems |
| title_sub | modeling, analysis, and design for simple mechanical control systems |
| topic | Commande automatique Controle automático larpcal Física matemática larpcal Geometria diferencial larpcal Géométrie différentielle Automatic control Geometry, Differential Mechanisches System (DE-588)4132811-5 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
| topic_facet | Commande automatique Controle automático Física matemática Geometria diferencial Géométrie différentielle Automatic control Geometry, Differential Mechanisches System Kontrolltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015358332&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002476038 |
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