Numerical methods for the investigation of periodic motions in multibody system dynamics: a collocation approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Aachen
Shaker
1998
|
| Ausgabe: | Als Ms. gedr. |
| Schriftenreihe: | Berichte aus der Mathematik
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Zugl.: Ulm, Univ., Diss., 1998 |
| Beschreibung: | V, 170 S. graph. Darst. |
| ISBN: | 3826540611 |
Internformat
MARC
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| 245 | 1 | 0 | |a Numerical methods for the investigation of periodic motions in multibody system dynamics |b a collocation approach |c Cornelia Franke |
| 250 | |a Als Ms. gedr. | ||
| 264 | 1 | |a Aachen |b Shaker |c 1998 | |
| 300 | |a V, 170 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Berichte aus der Mathematik | |
| 500 | |a Zugl.: Ulm, Univ., Diss., 1998 | ||
| 650 | 0 | 7 | |a Differential-algebraisches Gleichungssystem |0 (DE-588)4229517-8 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Kollokationsmethode |0 (DE-588)4164696-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Periodische Lösung |0 (DE-588)4199269-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mehrkörpersystem |0 (DE-588)4038390-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Periodische Bewegung |0 (DE-588)4173778-7 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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| adam_text |
CONTENTS
ZUSAMMENFASSUNG
VII
NOTATION
X
INTRODUCTION
AND
SUMMARY
1
1
MULTIBODY
SYSTEMS
AND
DIFFERENTIAL-ALGEBRAIC
EQUATIONS
4
1.1
EQUATIONS
OF
MOTION
OF
MULTIBODY
SYSTEMS
.
4
1.2
DIFFERENTIAL-ALGEBRAIC
EQUATIONS
.
7
1.2.1
FUNDAMENTALS
.
7
1.2.2
EQUATIONS
OF
MOTION
AS
DIFFERENTIAL-ALGEBRAIC
EQUATIONS
.
11
1.3
EXAMPLE:
THE
WHEELSET
.
16
2
PERIODIC
SOLUTIONS
OF
MULTIBODY
SYSTEMS
21
2.1
PERIODIC
SOLUTIONS
.
22
2.1.1
BASIC
TERMS
.
22
2.1.2
THE
BOUNDARY
VALUE
PROBLEM
.
23
2.2
POINCARE
MAPS
.
24
2.3
STABILITY
OF
PERIODIC
SOLUTIONS
.
26
2.3.1
BASIC
TERMS
.
26
2.3.2
MONODROMY
MATRICES
AND
FLOQUET
MULTIPLIERS
.
27
2.3.3
STABILITY
AND
FLOQUET
MULTIPLIERS
.
31
IV
CONTENTS
2.3.4
ISOLATION
OF
PERIODIC
SOLUTIONS
.
33
2.3.5
FLOQUET
MULTIPLIERS
FOR
SYSTEMS
WITH
REDUCED
INDEX
.
36
2.3.6
MONODROMY
MATRICES
AND
PROJECTIONS
.
43
2.4
PERIODIC
BRANCHES
AND
BIFURCATIONS
.
45
2.4.1
PERIODIC
BRANCHES
.
46
2.4.2
HOPF
BIFURCATIONS
.
48
2.4.3
BIFURCATIONS
ON
PERIODIC
BRANCHES
.
51
2.5
TEST
EXAMPLE:
THE
HOPF
PENDULUM
.
53
3
NUMERICAL
INVESTIGATION
OF
PERIODIC
SOLUTIONS
OF
MULTIBODY
SYSTEMS
56
3.1
NUMERICAL
METHODS
TO
APPROXIMATE
PERIODIC
SOLUTIONS
.
56
3.1.1
MULTIPLE
SHOOTING
METHODS
.
58
3.1.2
FINITE
DIFFERENCE
METHODS
.
61
3.1.3
HARMONIC
BALANCE
.
63
3.2
PROBLEM
FORMULATION:
THE
INDEX-2
BOUNDARY
VALUE
PROBLEM
.
65
3.3
STABILITY
ANALYSIS
.
67
3.4
PROJECTED
COLLOCATION
.
76
3.4.1
THE
PROJECTED
COLLOCATION
EQUATIONS
.
77
3.4.2
LINEAR
PROJECTED
COLLOCATION
.
82
3.4.3
NONLINEAR
PROJECTED
COLLOCATION
.
94
3.5
APPROXIMATION
OF
FLOQUET
MULTIPLIERS
.
104
3.6
CONTINUATION
OF
PERIODIC
BRANCHES
AND
BIFURCATIONS
.
107
3.6.1
CONTINUATION
METHODS
.
108
3.6.2
DETECTION
OF
BIFURCATIONS
ON
PERIODIC
BRANCHES
.
112
3.6.3
STARTING
AT
HOPF
BIFURCATIONS
.
112
4
ALGORITHMS
AND
IMPLEMENTATION
DETAILS
114
4.1
FUNDAMENTALS
.
114
CONTENTS
V
4.2
SOLVING
THE
LINEARIZED
SYSTEM
.
116
4.2.1
CONDENSATION
OF
PARAMETERS
.
117
4.2.2
PROJECTION
.
117
4.2.3
SOLVING
THE
GLOBAL
LINEAR
SYSTEM
.
119
4.2.4
APPROXIMATION
OF
FLOQNET
MULTIPLIERS
.
121
4.2.5
THE
ALGORITHM
.
122
4.3
SOLVING
THE
NONLINEAR
SYSTEM
.
123
4.4
MESH
SELECTION
.
124
4.4.1
THE
MESH
SELECTION
PROBLEM
.
124
4.4.2
ERROR
EQUIDISTRIBUTION
AND
MONITORING
.
126
4.4.3
ERROR
ESTIMATION
.
129
4.4.4
MESH
SELECTION
AND
CONTINUATION
.
132
4.4.5
THE
ALGORITHM
.
133
4.5
CONTINUATION
AND
BIFURCATIONS
.
136
4.5.1
CONTINUATION
OF
PERIODIC
BRANCHES
.
136
4.5.2
HOPF
BIFURCATIONS
.
138
5
NUMERICAL
TESTS
AND
EXAMPLES
140
5.1
THE
HOPF
PENDULUM
.
140
5.2
THE
WHEELSET
.
150
CONCLUSIONS
160
A
AN
AUXILIARY
THEOREM
162
REFERENCES
165 |
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| id | DE-604.BV012120985 |
| illustrated | Illustrated |
| indexdate | 2024-08-14T00:18:35Z |
| institution | BVB |
| isbn | 3826540611 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008208520 |
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| physical | V, 170 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
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| publisher | Shaker |
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| series2 | Berichte aus der Mathematik |
| spelling | Franke, Cornelia Verfasser aut Numerical methods for the investigation of periodic motions in multibody system dynamics a collocation approach Cornelia Franke Als Ms. gedr. Aachen Shaker 1998 V, 170 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Berichte aus der Mathematik Zugl.: Ulm, Univ., Diss., 1998 Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd rswk-swf Hopf-Verzweigung (DE-588)4160648-6 gnd rswk-swf Rad-Schiene-System (DE-588)4048245-5 gnd rswk-swf Dynamik (DE-588)4013384-9 gnd rswk-swf Kollokationsmethode (DE-588)4164696-4 gnd rswk-swf Periodische Lösung (DE-588)4199269-6 gnd rswk-swf Mehrkörpersystem (DE-588)4038390-8 gnd rswk-swf Periodische Bewegung (DE-588)4173778-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Rad-Schiene-System (DE-588)4048245-5 s Mehrkörpersystem (DE-588)4038390-8 s Dynamik (DE-588)4013384-9 s Periodische Bewegung (DE-588)4173778-7 s Differential-algebraisches Gleichungssystem (DE-588)4229517-8 s DE-604 Periodische Lösung (DE-588)4199269-6 s Hopf-Verzweigung (DE-588)4160648-6 s Kollokationsmethode (DE-588)4164696-4 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008208520&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Franke, Cornelia Numerical methods for the investigation of periodic motions in multibody system dynamics a collocation approach Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd Hopf-Verzweigung (DE-588)4160648-6 gnd Rad-Schiene-System (DE-588)4048245-5 gnd Dynamik (DE-588)4013384-9 gnd Kollokationsmethode (DE-588)4164696-4 gnd Periodische Lösung (DE-588)4199269-6 gnd Mehrkörpersystem (DE-588)4038390-8 gnd Periodische Bewegung (DE-588)4173778-7 gnd |
| subject_GND | (DE-588)4229517-8 (DE-588)4160648-6 (DE-588)4048245-5 (DE-588)4013384-9 (DE-588)4164696-4 (DE-588)4199269-6 (DE-588)4038390-8 (DE-588)4173778-7 (DE-588)4113937-9 |
| title | Numerical methods for the investigation of periodic motions in multibody system dynamics a collocation approach |
| title_auth | Numerical methods for the investigation of periodic motions in multibody system dynamics a collocation approach |
| title_exact_search | Numerical methods for the investigation of periodic motions in multibody system dynamics a collocation approach |
| title_full | Numerical methods for the investigation of periodic motions in multibody system dynamics a collocation approach Cornelia Franke |
| title_fullStr | Numerical methods for the investigation of periodic motions in multibody system dynamics a collocation approach Cornelia Franke |
| title_full_unstemmed | Numerical methods for the investigation of periodic motions in multibody system dynamics a collocation approach Cornelia Franke |
| title_short | Numerical methods for the investigation of periodic motions in multibody system dynamics |
| title_sort | numerical methods for the investigation of periodic motions in multibody system dynamics a collocation approach |
| title_sub | a collocation approach |
| topic | Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd Hopf-Verzweigung (DE-588)4160648-6 gnd Rad-Schiene-System (DE-588)4048245-5 gnd Dynamik (DE-588)4013384-9 gnd Kollokationsmethode (DE-588)4164696-4 gnd Periodische Lösung (DE-588)4199269-6 gnd Mehrkörpersystem (DE-588)4038390-8 gnd Periodische Bewegung (DE-588)4173778-7 gnd |
| topic_facet | Differential-algebraisches Gleichungssystem Hopf-Verzweigung Rad-Schiene-System Dynamik Kollokationsmethode Periodische Lösung Mehrkörpersystem Periodische Bewegung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008208520&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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