Elastic multibody dynamics: a direct Ritz approach
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
[Dordrecht]
Springer
2008
|
| Series: | Intelligent systems, control and automation
35 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 449 S. Ill., graph. Darst. |
| ISBN: | 9781402086793 |
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MARC
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| 100 | 1 | |a Bremer, Hartmut |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Elastic multibody dynamics |b a direct Ritz approach |c H. Bremer |
| 264 | 1 | |a [Dordrecht] |b Springer |c 2008 | |
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Record in the Search Index
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| adam_text | H. BREMER ELASTIC MULTIBODY DYNAMICS A DIRECT RITZ APPROACH SPRINGER
TABLE OF CONTENTS 1. INTRODUCTION 1 1.1 BACKGROUND 1 1.2 CONTENTS 5 2.
AXIOMS AND PRINCIPLES 7 2.1 AXIOMS 7 2.2 PRINCIPLES - THE DIFFERENTIAL
FORM 7 2.3 MINIMAL REPRESENTATION 15 2.3.1 VIRTUAL DISPLACEMENTS AND
VARIATIONS 16 2.3.2 MINIMAL COORDINATES AND MINIMAL VELOCITIES 18 2.3.3
THE TRANSITIVITY EQUATION 19 2.4 THE CENTRAL EQUATION OF DYNAMICS 20 2.5
PRINCIPLES - THE MINIMAL FORM 22 2.6 RHEONOMIC AND NON-HOLONOMIC
CONSTRAINTS 25 2.7 CONCLUSIONS 26 3. KINEMATICS 29 3.1 TRANSLATION AND
ROTATION 29 3.1.1 ROTATION AXIS AND ROTATION ANGLE 30 3.1.2
TRANSFORMATION MATRICES 33 3.1.2.1 ROTATION VECTOR REPRESENTATION 33
3.1.2.2 CARDAN ANGLE REPRESENTATION 34 3.1.2.3 EULER ANGLE
REPRESENTATION 36 3.1.3 COMPARISON 36 3.2 VELOCITIES 39 3.2.1 ANGULAR
VELOCITY 40 3.2.1.1 GENERAL PROPERTIES 40 3.2.1.2 ROTATION VECTOR
REPRESENTATION 41 3.2.1.3 CARDAN ANGLE REPRESENTATION 42 3.2.1.4 EULER
ANGLE REPRESENTATION 43 V VI TABLE OF CONTENTS 3.3 3.4 3.5 3.6 STATE
SPACE 3.3.1 KINEMATIC DIFFERENTIAL EQUATIONS 3.3.1.1 ROTATION VECTOR
REPRESENTATION 3.3.1.2 CARDAN ANGLE REPRESENTATION 3.3.1.3 EULER ANGLE
REPRESENTATION 3.3.2 SUMMARY ROTATIONS ACCELERATIONS TOPOLOGY - THE
KINEMATIC CHAIN DISCUSSION RIGID MULTIBODY SYSTEMS 4.1 4.2 4.3 4.4 4.5
MODELING ASPECTS 4.1.1 ON MASS POINT DYNAMICS 4.1.2 THE RIGIDITY
CONDITION MULTIBODY SYSTEMS 4.2.1 KINETIC ENERGY 4.2.2 POTENTIALS
4.2.2.1 GRAVITATION 4.2.2.2 SPRINGS 4.2.3 RAYLEIGH S FUNCTION 4.2.4
TRANSITIVITY EQUATION 4.2.5 THE PROJECTION EQUATION THE TRIANGLE OF
METHODS 4.3.1 ANALYTICAL METHODS 4.3.2 SYNTHETIC PROCEDURE(S) 4.3.3
ANALYTICAL VS. SYNTHETIC METHOD(S) SUBSYSTEMS 4.4.1 BASIC ELEMENT: THE
RIGID BODY 4.4.1.1 SPATIAL MOTION 4.4.1.2 PLANE MOTION 4.4.2 SUBSYSTEM
ASSEMBLAGE 4.4.2.1 ABSOLUTE VELOCITIES 4.4.2.2 RELATIVE VELOCITIES
4.4.2.3 PRISMATIC JOINT/REVOLUTE JOINT - SPATIAL MOTION 4.4.3 SYNTHESIS
4.4.3.1 MINIMAL REPRESENTATION 4.4.3.2 RECURSIVE REPRESENTATION
CONSTRAINTS 4.5.1 INNER CONSTRAINTS 4.5.2 ADDITIONAL CONSTRAINTS 4.5.2.1
JACOBI EQUATION 4.5.2.2 MINIMAL REPRESENTATION 4.5.2.3 RECURSIVE
REPRESENTATION 4.5.2.4 CONSTRAINT STABILIZATION 44 45 45 46 46 47 49 50
56 59 59 59 61 65 65 66 66 67 68 69 70 71 71 73 75 78 78 78 82 85 85 88
89 91 93 95 100 100 101 102 103 104 107 TABLE OF CONTENTS VLL 4.6
SEGMENTATION: ELASTIC BODY REPRESENTATION 109 4.6.1 CHAIN AND THREAD
(PLANE MOTION) 109 4.6.2 CHAIN, THREAD, AND BEAM 111 4.7 CONCLUSION 113
5. ELASTIC MULTIBODY SYSTEMS - THE PARTIAL DIFFERENTIAL EQUATIONS 115
5.1 ELASTIC POTENTIAL 115 5.1.1 LINEAR ELASTICITY 116 5.1.2 INNER
CONSTRAINTS, CLASSIFICATION OF ELASTIC BODIES 117 5.1.3 DISK AND PLATE
119 5.1.4 BEAM 121 5.2 KINETIC ENERGY 123 5.3 CHECKING PROCEDURES 124
5.3.1 HAMILTON S PRINCIPLE AND THE ANALYTICAL METHODS 124 5.3.2
PROJECTION EQUATION 131 5.4 SINGLE ELASTIC BODY - SMALL MOTION
AMPLITUDES 133 5.4.1 BEAMS 133 5.4.2 SHELLS AND PLATES 153 5.5 SINGLE
BODY - GROSS MOTION 159 5.5.1 THE ELASTIC ROTOR 159 5.5.2 THE HELICOPTER
BLADE (1) 162 5.6 DYNAMICAL STIFFENING 167 5.6.1 THE CAUCHY STRESS
TENSOR 167 5.6.2 THE TREFFTZ (OR 2ND PIOLA-KIRCHHOFF) STRESS TENSOR 167
5.6.3 SECOND-ORDER BEAM DISPLACEMENT FIELDS 173 5.6.4 DYNAMICAL
STIFFENING MATRIX 177 5.6.5 THE HELICOPTER BLADE (2) 183 5.7 MULTIBODY
SYSTEMS - GROSS MOTION 190 5.7.1 THE KINEMATIC CHAIN 190 5.7.2 MINIMAL
VELOCITIES 193 5.7.3 MOTION EQUATIONS 194 5.7.3.1 DYNAMICAL STIFFENING
195 5.7.3.2 EQUATIONS OF MOTION 196 5.7.4 BOUNDARY CONDITIONS 210 5.8
CONCLUSION 214 6. ELASTIC MULTIBODY SYSTEMS - THE SUBSYSTEM ORDINARY
DIFFERENTIAL EQUATIONS 219 6.1 GALERKIN METHOD 219 6.1.1 DIRECT GALERKIN
METHOD 219 6.1.2 EXTENDED GALERKIN METHOD 224 6.2 (DIRECT) RITZ METHOD
225 6.3 RAYLEIGH QUOTIENT 229 VLLL TABLE OF CONTENTS 6.4 SINGLE ELASTIC
BODY - SMALL MOTION AMPLITUDES 235 6.4.1 PLATE 235 6.4.1.1 EQUATIONS OF
MOTION 235 6.4.1.2 BASICS 236 6.4.1.3 SHAPE FUNCTIONS: SPATIAL
SEPARATION APPROACH 238 6.4.1.4 EXPANSION IN TERMS OF BEAM FUNCTIONS 239
6.4.1.5 CONVERGENCE AND SOLUTION 243 6.4.2 TORSIONAL SHAFT 246 6.4.2.1
EIGENFUNCTIONS 246 6.4.2.2 MOTION EQUATIONS 247 6.4.2.3 SHAPE FUNCTIONS
249 6.4.3 CHANGE-OVER GEAR 253 6.5 SINGLE ELASTIC BODY - GROSS MOTION
255 6.5.1 THE ELASTIC ROTOR 255 6.5.1.1 RHEONOMIC CONSTRAINT 257 6.5.1.2
CHOICE OF SHAPE FUNCTIONS - PROLATE ROTOR (Q, - 0) 259 6.5.1.3 CHOICE OF
SHAPE FUNCTIONS - OBLATE ROTOR (* = 0) 264 6.5.1.4 CONFIGURATION SPACE
AND STATE SPACE (FL * 0) 271 6.5.1.5 THE LAVAL- (OR JEFFCOTT-) ROTOR 272
6.5.1.6 ROTOR WITH FIXED POINT 277 6.5.1.7 ELASTIC ROTOR PROPERTIES 283
6.6 GROSS MOTION - DYNAMICAL STIFFENING (RITZ APPROACH) 290 6.6.1
ROTATING BEAM - ONE-LINK ELASTIC ROBOT 291 6.6.1.1 MASS MATRIX 293
6.6.1.2 RESTORING MATRIX 293 6.6.1.3 EQUATIONS OF MOTION 295 6.6.2
TRANSLATING BEAM - ELASTIC TT-ROBOT 296 6.6.2.1 MASS MATRIX 305 6.6.2.2
RESTORING MATRIX 305 6.6.2.3 EQUATIONS OF MOTION 306 6.6.2.4 SIMPLIFIED
SYSTEM 306 6.7 THE MASS MATRIX RECONSIDERED (RITZ APPROACH) 311 6.8 THE
G-MATRIX RECONSIDERED (RITZ APPROACH) 315 6.9 CONCLUSIONS 321 7. ELASTIC
MULTIBODY SYSTEMS - ORDINARY DIFFERENTIAL EQUATIONS 327 7.1 SUMMARY
PROCEDURE 327 7.1.1 RIGID MULTIBODY SYSTEMS 327 7.1.2 ELASTIC MULTIBODY
SYSTEMS 329 7.2 MIXED RIGID-ELASTIC MULTIBODY SYSTEMS 335 7.3
APPLICATIONS 338 7.3.1 PRISMATIC JOINT - THE TELESCOPING ARM 338 7.3.1.1
ON MASS DISTRIBUTION: TIP BODY INFLUENCE 339 TABLE OF CONTENTS IX
7.3.1.2 SUBSYSTEM EQUATIONS 340 7.3.1.3 THE KINEMATIC CHAIN 345 7.3.2
REVOLUTE JOINT 346 7.3.2.1 SUBSYSTEM EQUATIONS 346 7.3.2.2 THE KINEMATIC
CHAIN 347 7.3.3 SPATIAL MOTION 348 7.3.4 PLANE MOTION 350 7.4 PLANE
MOTION - RECALCULATION 352 7.4.1 MINIMAL VELOCITIES AND PROJECTION 352
7.4.2 SUBSYSTEM MATRICES 354 7.4.3 DYNAMICAL STIFFENING 359 7.4.4 THE
KINEMATIC CHAIN 361 7.5 REDUCED NUMBER OF SHAPE FUNCTIONS: CONTROLLED
SYSTEMS 369 7.6 REMARK ON CONTROLLED SYSTEMS 380 8. A SHORT EXCURSION
INTO STABILITY AND CONTROL 383 8.1 OPTIMALITY 383 8.1.1 RESULTS FROM
CLASSICAL OPTIMIZATION THEORY 387 8.1.2 RICCATI- (OR LQR-) CONTROL 388
8.1.3 CONTROL PARAMETER OPTIMIZATION 390 8.2 STABILITY 391 8.3 LINEAR
TIME-INVARIANT SYSTEMS 395 8.3.1 FUNDAMENTAL (OR TRANSITION) MATRIX 395
8.3.2 THEOREM OF CAYLEY AND HAMILTON 399 8.3.3 STABILITY THEOREM FOR
MECHANICAL SYSTEMS 401 8.4 STABILIZATION OF MECHANICAL SYSTEMS 406 8.5
OBSERVERS 411 8.5.1 BASIC NOTATION 411 8.5.2 COMPLETE STATE OBSERVER FOR
CONTROL 413 8.5.3 DISTURBANCE SUPPRESSION ( HIGH GAIN OBSERVER ) 416
8.5.4 DISTURBANCE OBSERVATION 419 8.6 DECENTRALIZED CONTROL 423 8.7 ON
CONTROL INPUT VARIABLES 426 REFERENCES 431 LIST OF SYMBOLS 437 INDEX 445
|
| any_adam_object | 1 |
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| author_facet | Bremer, Hartmut |
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| building | Verbundindex |
| bvnumber | BV025561888 |
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| discipline | Physik |
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| id | DE-604.BV025561888 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:36:32Z |
| institution | BVB |
| isbn | 9781402086793 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020161200 |
| oclc_num | 254621319 |
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| owner | DE-11 |
| owner_facet | DE-11 |
| physical | IX, 449 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | Intelligent systems, control and automation |
| series2 | Intelligent systems, control and automation: science and engineering |
| spelling | Bremer, Hartmut Verfasser aut Elastic multibody dynamics a direct Ritz approach H. Bremer [Dordrecht] Springer 2008 IX, 449 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Intelligent systems, control and automation: science and engineering 35 Elastizität (DE-588)4014159-7 gnd rswk-swf Mehrkörpersystem (DE-588)4038390-8 gnd rswk-swf Mehrkörpersystem (DE-588)4038390-8 s Elastizität (DE-588)4014159-7 s DE-604 Intelligent systems, control and automation 35 (DE-604)BV024977557 35 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020161200&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bremer, Hartmut Elastic multibody dynamics a direct Ritz approach Intelligent systems, control and automation Elastizität (DE-588)4014159-7 gnd Mehrkörpersystem (DE-588)4038390-8 gnd |
| subject_GND | (DE-588)4014159-7 (DE-588)4038390-8 |
| title | Elastic multibody dynamics a direct Ritz approach |
| title_auth | Elastic multibody dynamics a direct Ritz approach |
| title_exact_search | Elastic multibody dynamics a direct Ritz approach |
| title_full | Elastic multibody dynamics a direct Ritz approach H. Bremer |
| title_fullStr | Elastic multibody dynamics a direct Ritz approach H. Bremer |
| title_full_unstemmed | Elastic multibody dynamics a direct Ritz approach H. Bremer |
| title_short | Elastic multibody dynamics |
| title_sort | elastic multibody dynamics a direct ritz approach |
| title_sub | a direct Ritz approach |
| topic | Elastizität (DE-588)4014159-7 gnd Mehrkörpersystem (DE-588)4038390-8 gnd |
| topic_facet | Elastizität Mehrkörpersystem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020161200&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV024977557 |
| work_keys_str_mv | AT bremerhartmut elasticmultibodydynamicsadirectritzapproach |