Periodic solutions of nonlinear dynamical systems: numerical computation, stability, bifurcation and transition to chaos
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1991
|
| Series: | Lecture notes in mathematics
1483 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 171 S. graph. Darst. |
| ISBN: | 3540545123 0387545123 |
Staff View
MARC
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| 100 | 1 | |a Reithmeier, Eduard |d 1957- |e Verfasser |0 (DE-588)1145579019 |4 aut | |
| 245 | 1 | 0 | |a Periodic solutions of nonlinear dynamical systems |b numerical computation, stability, bifurcation and transition to chaos |c Eduard Reithmeier |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1991 | |
| 300 | |a VI, 171 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1483 | |
| 502 | |a Zugl.: München, TU, Diss., 1989 | ||
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Record in the Search Index
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| adam_text | Contents
1 Introduction 3
1.1 Motivation and objective 3
1.2 Survey of literature 6
1.2.1 Existence of periodic solutions 6
1.2.2 Numerical computation of periodic solutions 7
1.2.3 Bifurcation and stability of periodic solutions 7
1.2.4 Periodic solutions of dynamical systems with discontinuities . 8
2 Differentiable dynamical systems 9
2.1 Preliminary remarks 9
2.2 Some basic structures and properties of the equation of motion of
dynamical systems 17
2.2.1 Periodicity of configuration space coordinates 17
2.2.2 Analyticity of the dynamical system 17
2.2.3 Representation in state space coordinates 18
2.2.4 Singular points 19
2.3 Normal forms of non resonant vector fields 20
2.4 Classification of singularities 33
2.4.1 Corank, critical and noncritical variables 35
2.4.2 Codimension, specification of the singularities 35
2.4.3 Structural stability 44
2.5 Periodic solutions of HAMILTONian systems 45
2.5.1 The boundary value problem for periodic solutions of HAMIL¬
TONian systems 46
2.5.2 The problem of the translation invariance of periodic solutions
of autonomous systems 49
2.5.3 Formulation of the BVP with fixed endpoint 53
2.5.4 Numerical computation of periodic solutions of the double
pendulum 54
2.6 Periodic solutions of dissipative and excited systems 66
2.6.1 Numerical computation of limit cycles 66
2.6.2 Example: Wheel set of a railway vehicle 68
2.7 Periodic solutions with additional properties 76
2 CONTENTS
2.7.1 Definition of the problem 76
2.7.2 Formulation of the problem as a boundary value problem ... 79
2.7.3 Singularities of the HAMILTONian system of optimization . . 80
2.7.4 Examples of application 81
2.8 Stability and bifurcation of periodic solutions 85
2.8.1 Monodromy matrix and stability of a periodic solution .... 89
2.8.2 HOPF—bifurcation as consequence of loss of stability 94
2.8.3 Necessary conditions for bifurcation 100
2.8.4 Stability and bifurcation in HAMILTONian systems 104
3 Differentiable dynamical systems with discontinuities 110
3.1 The recursive description 119
3.2 Periodic solutions of recursively described systems 131
3.2.1 Definition of a periodic solution 131
3.2.2 Invariance of translation of a periodic solution 132
3.2.3 Numerical computation of periodic solutions 132
3.3 Stability and bifurcation of a sequence of recursively computed points 140
3.3.1 Definition of stability 140
3.3.2 Existence of periodic solutions inside stability domains .... 140
3.3.3 Monodromy matrix of a (m : n) cycle 141
3.3.4 Bifurcation as a consequence of loss of stability 141
4 Literature 152
5 Appendix dataset 163
6 Index 165
|
| any_adam_object | 1 |
| author | Reithmeier, Eduard 1957- |
| author_GND | (DE-588)1145579019 |
| author_facet | Reithmeier, Eduard 1957- |
| author_role | aut |
| author_sort | Reithmeier, Eduard 1957- |
| author_variant | e r er |
| building | Verbundindex |
| bvnumber | BV004703857 |
| classification_rvk | SI 850 |
| classification_tum | MAT 344f |
| ctrlnum | (OCoLC)260182091 (DE-599)BVBBV004703857 |
| discipline | Mathematik |
| format | Thesis Book |
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| id | DE-604.BV004703857 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:16:22Z |
| institution | BVB |
| isbn | 3540545123 0387545123 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002889731 |
| oclc_num | 260182091 |
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| physical | VI, 171 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Reithmeier, Eduard 1957- Verfasser (DE-588)1145579019 aut Periodic solutions of nonlinear dynamical systems numerical computation, stability, bifurcation and transition to chaos Eduard Reithmeier Berlin [u.a.] Springer 1991 VI, 171 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1483 Zugl.: München, TU, Diss., 1989 Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Periodische Lösung (DE-588)4199269-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Nichtlineares dynamisches System (DE-588)4126142-2 s Periodische Lösung (DE-588)4199269-6 s DE-604 Lecture notes in mathematics 1483 (DE-604)BV000676446 1483 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002889731&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Reithmeier, Eduard 1957- Periodic solutions of nonlinear dynamical systems numerical computation, stability, bifurcation and transition to chaos Lecture notes in mathematics Nichtlineares dynamisches System (DE-588)4126142-2 gnd Periodische Lösung (DE-588)4199269-6 gnd |
| subject_GND | (DE-588)4126142-2 (DE-588)4199269-6 (DE-588)4113937-9 |
| title | Periodic solutions of nonlinear dynamical systems numerical computation, stability, bifurcation and transition to chaos |
| title_auth | Periodic solutions of nonlinear dynamical systems numerical computation, stability, bifurcation and transition to chaos |
| title_exact_search | Periodic solutions of nonlinear dynamical systems numerical computation, stability, bifurcation and transition to chaos |
| title_full | Periodic solutions of nonlinear dynamical systems numerical computation, stability, bifurcation and transition to chaos Eduard Reithmeier |
| title_fullStr | Periodic solutions of nonlinear dynamical systems numerical computation, stability, bifurcation and transition to chaos Eduard Reithmeier |
| title_full_unstemmed | Periodic solutions of nonlinear dynamical systems numerical computation, stability, bifurcation and transition to chaos Eduard Reithmeier |
| title_short | Periodic solutions of nonlinear dynamical systems |
| title_sort | periodic solutions of nonlinear dynamical systems numerical computation stability bifurcation and transition to chaos |
| title_sub | numerical computation, stability, bifurcation and transition to chaos |
| topic | Nichtlineares dynamisches System (DE-588)4126142-2 gnd Periodische Lösung (DE-588)4199269-6 gnd |
| topic_facet | Nichtlineares dynamisches System Periodische Lösung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002889731&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT reithmeiereduard periodicsolutionsofnonlineardynamicalsystemsnumericalcomputationstabilitybifurcationandtransitiontochaos |