Bifurcation and chaos in nonsmooth mechanical systems /:
This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysi...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; River Edge, NJ :
World Scientific,
2003.
|
| Schriftenreihe: | World Scientific series on nonlinear science. Monographs and treatises ;
v. 45. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical and computational developments. |
| Beschreibung: | 1 online resource (xvii, 543 pages :) |
| Bibliographie: | Includes bibliographical references (pages 507-530) and index. |
| ISBN: | 9812564802 9789812564801 |
Internformat
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocm61048703 | ||
| 003 | OCoLC | ||
| 005 | 20240705115654.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 050718s2003 si a ob 001 0 eng d | ||
| 040 | |a N$T |b eng |e pn |c N$T |d OCLCQ |d YDXCP |d OCLCQ |d IDEBK |d OCLCQ |d OCLCO |d OCLCQ |d OCLCA |d OCLCF |d I9W |d OCLCA |d NLGGC |d OCLCQ |d MERUC |d EBLCP |d OCLCQ |d AGLDB |d ZCU |d OCLCQ |d U3W |d OCLCQ |d VTS |d ICG |d INT |d OCLCQ |d COCUF |d OCLCQ |d STF |d G3B |d DKC |d AU@ |d OCLCQ |d UKAHL |d OCLCQ |d K6U |d LEAUB |d OCLCO |d OCLCQ |d OCLCO |d OCLCL |d SXB |d OCLCQ |d OCLCO | ||
| 019 | |a 437147498 |a 1086431974 | ||
| 020 | |a 9812564802 |q (electronic bk.) | ||
| 020 | |a 9789812564801 |q (electronic bk.) | ||
| 020 | |z 9812384596 | ||
| 020 | |z 9789812384591 | ||
| 035 | |a (OCoLC)61048703 |z (OCoLC)437147498 |z (OCoLC)1086431974 | ||
| 050 | 4 | |a QA380 |b .A9 2003eb | |
| 072 | 7 | |a MAT |x 007000 |2 bisacsh | |
| 082 | 7 | |a 515/.35 |2 22 | |
| 049 | |a MAIN | ||
| 100 | 1 | |a Awrejcewicz, J. |q (Jan) |1 https://id.oclc.org/worldcat/entity/E39PBJr83fkjVcwR6tgHmDBHG3 |0 http://id.loc.gov/authorities/names/n88212452 | |
| 245 | 1 | 0 | |a Bifurcation and chaos in nonsmooth mechanical systems / |c Jan Awrejcewicz, Claude-Henri Lamarque. |
| 260 | |a Singapore ; |a River Edge, NJ : |b World Scientific, |c 2003. | ||
| 300 | |a 1 online resource (xvii, 543 pages :) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a World Scientific series on nonlinear science. Series A, Monographs and treatises ; |v v. 45 | |
| 504 | |a Includes bibliographical references (pages 507-530) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 1. Introduction to discontinuous ODEs. 1.1. Introduction. 1.2. Filippov's theory. 1.3. Aizerman's theory. 1.4. Examples. 1.5. Boundary value problem -- 2. Mathematical background for multivalued formulations. 2.1. Origin of nonlinearities. 2.2. Smooth and nonsmooth nonlinearities. 2.3. Examples and dynamical equilibria. 2.4. Existence and uniqueness. 2.5. Stochastic frame -- 3. Numerical schemes and analytical methods. 3.1. Numerical schemes. 3.2. Analytical methods -- 4. Properties of numerical schemes. 4.1. Dynamics of systems with friction or elastoplastic terms. 4.2. Systems with impacts. 4.3. Conclusion -- 5. Bifurcations of a particular van der Pol-Duffing oscillator. 5.1. The analysed system and the averaged equations. 5.2. "0" type bifurcations. 5.3. Complex bifurcations. 5.4. Observations of strange attractors using numerical simulations -- 6. Stick-slip oscillator with two degrees of freedom. 6.1. Introduction. 6.2. Disc -- flexible arm oscillator. 6.3. Two horizontally situated masses -- 7. Piecewise linear approximations. 7.1. Introduction. 7.2. Exact and approximated models. 7.3. Approximation and global dynamic behavior. 7.4. Numerical results. 7.5. Conclusion -- 8. Chua's circuit with discontinuities. 8.1. Introduction. 8.2. Mechanical realizations of Chua's circuit. 8.3. Generalized double scroll Chua's circuit -- 9. Mechanical system with impacts and modal approaches. 9.1. Introduction. 9.2. Single degree of freedom system. 9.3. Two degrees of freedom systems. 9.4. Conclusion -- 10. One DOF mechanical system with friction. 10.1. Introduction. 10.2. Modelling the pendulum with friction. 10.3. Numerical results. 10.4. The Melnikov analysis. 10.5. Conclusion. | |
| 505 | 8 | |a 11. Modelling the dynamical behaviour of elasto-plastic systems. 11.1. Rheological systems with "friction" -- 12. A mechanical system with 7 DOF. 12.1. Mathematical model. 12.2. Numerical results and comments for finite k3 -- 13. Stability of singular periodic motions in single degree of freedom vibro-impact oscillators and grazing bifurcations. 13.1. Introduction. 13.2. Mechanical system and change of coordinates. 13.3. Local expansion of the Poincaré map. 13.4. Stability of the nondifferentiable fixed point. 13.5. Applications. 13.6. Conclusion -- 14. Triple pendulum with impacts. 14.1. Introduction. 14.2. Investigated pendulum and governing equations (without impacts). 14.3. Introduction of the obstacles. 14.4. Calculation of the fundamental solution matrices for dynamical systems with impacts. 14.5. Simplification of the system. 14.6. The method used for integration of the system and its accuracy. 14.7. Numerical examples. 14.8. Concluding remarks -- 15. Analytical prediction of stick-slip chaos. 15.1. Introduction. 15.2. The Melnikov's method. 15.3. Analyzed system. 15.4. Analytical results -- 16. Thermoelasticity, wear and stick-slip movements of a rotating shaft with a rigid bush. 16.1. Introduction -- 17. Control for discrete models of buildings including elastoplastic terms. 17.1. Introduction. 17.2. Reminder about Prandtl rheological model. 17.3. The studied models with n DOF. 17.4. Existence and uniqueness results. 17.5. Numerical scheme. 17.6. Control procedure. 17.7. Algorithm of control. 17.8 Numerical results for a system with 3 DOF. 17.9. Extension to nonlinear cases. 17.10. Conclusion. | |
| 520 | |a This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical and computational developments. | ||
| 650 | 0 | |a Bifurcation theory. |0 http://id.loc.gov/authorities/subjects/sh85013940 | |
| 650 | 0 | |a Chaotic behavior in systems. |0 http://id.loc.gov/authorities/subjects/sh85022562 | |
| 650 | 0 | |a Differential equations, Nonlinear. |0 http://id.loc.gov/authorities/subjects/sh85037906 | |
| 650 | 6 | |a Théorie de la bifurcation. | |
| 650 | 6 | |a Chaos. | |
| 650 | 6 | |a Équations différentielles non linéaires. | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x General. |2 bisacsh | |
| 650 | 7 | |a Bifurcation theory |2 fast | |
| 650 | 7 | |a Chaotic behavior in systems |2 fast | |
| 650 | 7 | |a Differential equations, Nonlinear |2 fast | |
| 700 | 1 | |a Lamarque, Claude-Henri. |1 https://id.oclc.org/worldcat/entity/E39PCjCjcGqWkGPkqKytFJWMT3 |0 http://id.loc.gov/authorities/names/nr2003036751 | |
| 758 | |i has work: |a Bifurcation and chaos in nonsmooth mechanical systems (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGj9ybF3Dyx4RtYJ3xpVRX |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Awrejcewicz, J. (Jan). |t Bifurcation and chaos in nonsmooth mechanical systems. |d Singapore ; River Edge, NJ : World Scientific, 2003 |z 9812384596 |w (OCoLC)53362322 |
| 830 | 0 | |a World Scientific series on nonlinear science. |n Series A, |p Monographs and treatises ; |v v. 45. |0 http://id.loc.gov/authorities/names/no94008495 | |
| 856 | 1 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=135170 |3 Volltext | |
| 856 | 1 | |l CBO01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=135170 |3 Volltext | |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH21190640 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL234346 | ||
| 938 | |a EBSCOhost |b EBSC |n 135170 | ||
| 938 | |a YBP Library Services |b YANK |n 2407672 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocm61048703 |
|---|---|
| _version_ | 1813903283924762625 |
| adam_text | |
| any_adam_object | |
| author | Awrejcewicz, J. (Jan) |
| author2 | Lamarque, Claude-Henri |
| author2_role | |
| author2_variant | c h l chl |
| author_GND | http://id.loc.gov/authorities/names/n88212452 http://id.loc.gov/authorities/names/nr2003036751 |
| author_facet | Awrejcewicz, J. (Jan) Lamarque, Claude-Henri |
| author_role | |
| author_sort | Awrejcewicz, J. |
| author_variant | j a ja |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA380 |
| callnumber-raw | QA380 .A9 2003eb |
| callnumber-search | QA380 .A9 2003eb |
| callnumber-sort | QA 3380 A9 42003EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | 1. Introduction to discontinuous ODEs. 1.1. Introduction. 1.2. Filippov's theory. 1.3. Aizerman's theory. 1.4. Examples. 1.5. Boundary value problem -- 2. Mathematical background for multivalued formulations. 2.1. Origin of nonlinearities. 2.2. Smooth and nonsmooth nonlinearities. 2.3. Examples and dynamical equilibria. 2.4. Existence and uniqueness. 2.5. Stochastic frame -- 3. Numerical schemes and analytical methods. 3.1. Numerical schemes. 3.2. Analytical methods -- 4. Properties of numerical schemes. 4.1. Dynamics of systems with friction or elastoplastic terms. 4.2. Systems with impacts. 4.3. Conclusion -- 5. Bifurcations of a particular van der Pol-Duffing oscillator. 5.1. The analysed system and the averaged equations. 5.2. "0" type bifurcations. 5.3. Complex bifurcations. 5.4. Observations of strange attractors using numerical simulations -- 6. Stick-slip oscillator with two degrees of freedom. 6.1. Introduction. 6.2. Disc -- flexible arm oscillator. 6.3. Two horizontally situated masses -- 7. Piecewise linear approximations. 7.1. Introduction. 7.2. Exact and approximated models. 7.3. Approximation and global dynamic behavior. 7.4. Numerical results. 7.5. Conclusion -- 8. Chua's circuit with discontinuities. 8.1. Introduction. 8.2. Mechanical realizations of Chua's circuit. 8.3. Generalized double scroll Chua's circuit -- 9. Mechanical system with impacts and modal approaches. 9.1. Introduction. 9.2. Single degree of freedom system. 9.3. Two degrees of freedom systems. 9.4. Conclusion -- 10. One DOF mechanical system with friction. 10.1. Introduction. 10.2. Modelling the pendulum with friction. 10.3. Numerical results. 10.4. The Melnikov analysis. 10.5. Conclusion. 11. Modelling the dynamical behaviour of elasto-plastic systems. 11.1. Rheological systems with "friction" -- 12. A mechanical system with 7 DOF. 12.1. Mathematical model. 12.2. Numerical results and comments for finite k3 -- 13. Stability of singular periodic motions in single degree of freedom vibro-impact oscillators and grazing bifurcations. 13.1. Introduction. 13.2. Mechanical system and change of coordinates. 13.3. Local expansion of the Poincaré map. 13.4. Stability of the nondifferentiable fixed point. 13.5. Applications. 13.6. Conclusion -- 14. Triple pendulum with impacts. 14.1. Introduction. 14.2. Investigated pendulum and governing equations (without impacts). 14.3. Introduction of the obstacles. 14.4. Calculation of the fundamental solution matrices for dynamical systems with impacts. 14.5. Simplification of the system. 14.6. The method used for integration of the system and its accuracy. 14.7. Numerical examples. 14.8. Concluding remarks -- 15. Analytical prediction of stick-slip chaos. 15.1. Introduction. 15.2. The Melnikov's method. 15.3. Analyzed system. 15.4. Analytical results -- 16. Thermoelasticity, wear and stick-slip movements of a rotating shaft with a rigid bush. 16.1. Introduction -- 17. Control for discrete models of buildings including elastoplastic terms. 17.1. Introduction. 17.2. Reminder about Prandtl rheological model. 17.3. The studied models with n DOF. 17.4. Existence and uniqueness results. 17.5. Numerical scheme. 17.6. Control procedure. 17.7. Algorithm of control. 17.8 Numerical results for a system with 3 DOF. 17.9. Extension to nonlinear cases. 17.10. Conclusion. |
| ctrlnum | (OCoLC)61048703 |
| dewey-full | 515/.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.35 |
| dewey-search | 515/.35 |
| dewey-sort | 3515 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>07375cam a2200625 a 4500</leader><controlfield tag="001">ZDB-4-EBA-ocm61048703 </controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20240705115654.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cnu---unuuu</controlfield><controlfield tag="008">050718s2003 si a ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">N$T</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">N$T</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">YDXCP</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">IDEBK</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCA</subfield><subfield code="d">OCLCF</subfield><subfield code="d">I9W</subfield><subfield code="d">OCLCA</subfield><subfield code="d">NLGGC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">MERUC</subfield><subfield code="d">EBLCP</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AGLDB</subfield><subfield code="d">ZCU</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">U3W</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VTS</subfield><subfield code="d">ICG</subfield><subfield code="d">INT</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">COCUF</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">STF</subfield><subfield code="d">G3B</subfield><subfield code="d">DKC</subfield><subfield code="d">AU@</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UKAHL</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">K6U</subfield><subfield code="d">LEAUB</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield><subfield code="d">SXB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">437147498</subfield><subfield code="a">1086431974</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9812564802</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789812564801</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9812384596</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9789812384591</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)61048703</subfield><subfield code="z">(OCoLC)437147498</subfield><subfield code="z">(OCoLC)1086431974</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA380</subfield><subfield code="b">.A9 2003eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">007000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">515/.35</subfield><subfield code="2">22</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Awrejcewicz, J.</subfield><subfield code="q">(Jan)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PBJr83fkjVcwR6tgHmDBHG3</subfield><subfield code="0">http://id.loc.gov/authorities/names/n88212452</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Bifurcation and chaos in nonsmooth mechanical systems /</subfield><subfield code="c">Jan Awrejcewicz, Claude-Henri Lamarque.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Singapore ;</subfield><subfield code="a">River Edge, NJ :</subfield><subfield code="b">World Scientific,</subfield><subfield code="c">2003.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xvii, 543 pages :)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">World Scientific series on nonlinear science. Series A, Monographs and treatises ;</subfield><subfield code="v">v. 45</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 507-530) and index.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">1. Introduction to discontinuous ODEs. 1.1. Introduction. 1.2. Filippov's theory. 1.3. Aizerman's theory. 1.4. Examples. 1.5. Boundary value problem -- 2. Mathematical background for multivalued formulations. 2.1. Origin of nonlinearities. 2.2. Smooth and nonsmooth nonlinearities. 2.3. Examples and dynamical equilibria. 2.4. Existence and uniqueness. 2.5. Stochastic frame -- 3. Numerical schemes and analytical methods. 3.1. Numerical schemes. 3.2. Analytical methods -- 4. Properties of numerical schemes. 4.1. Dynamics of systems with friction or elastoplastic terms. 4.2. Systems with impacts. 4.3. Conclusion -- 5. Bifurcations of a particular van der Pol-Duffing oscillator. 5.1. The analysed system and the averaged equations. 5.2. "0" type bifurcations. 5.3. Complex bifurcations. 5.4. Observations of strange attractors using numerical simulations -- 6. Stick-slip oscillator with two degrees of freedom. 6.1. Introduction. 6.2. Disc -- flexible arm oscillator. 6.3. Two horizontally situated masses -- 7. Piecewise linear approximations. 7.1. Introduction. 7.2. Exact and approximated models. 7.3. Approximation and global dynamic behavior. 7.4. Numerical results. 7.5. Conclusion -- 8. Chua's circuit with discontinuities. 8.1. Introduction. 8.2. Mechanical realizations of Chua's circuit. 8.3. Generalized double scroll Chua's circuit -- 9. Mechanical system with impacts and modal approaches. 9.1. Introduction. 9.2. Single degree of freedom system. 9.3. Two degrees of freedom systems. 9.4. Conclusion -- 10. One DOF mechanical system with friction. 10.1. Introduction. 10.2. Modelling the pendulum with friction. 10.3. Numerical results. 10.4. The Melnikov analysis. 10.5. Conclusion.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">11. Modelling the dynamical behaviour of elasto-plastic systems. 11.1. Rheological systems with "friction" -- 12. A mechanical system with 7 DOF. 12.1. Mathematical model. 12.2. Numerical results and comments for finite k3 -- 13. Stability of singular periodic motions in single degree of freedom vibro-impact oscillators and grazing bifurcations. 13.1. Introduction. 13.2. Mechanical system and change of coordinates. 13.3. Local expansion of the Poincaré map. 13.4. Stability of the nondifferentiable fixed point. 13.5. Applications. 13.6. Conclusion -- 14. Triple pendulum with impacts. 14.1. Introduction. 14.2. Investigated pendulum and governing equations (without impacts). 14.3. Introduction of the obstacles. 14.4. Calculation of the fundamental solution matrices for dynamical systems with impacts. 14.5. Simplification of the system. 14.6. The method used for integration of the system and its accuracy. 14.7. Numerical examples. 14.8. Concluding remarks -- 15. Analytical prediction of stick-slip chaos. 15.1. Introduction. 15.2. The Melnikov's method. 15.3. Analyzed system. 15.4. Analytical results -- 16. Thermoelasticity, wear and stick-slip movements of a rotating shaft with a rigid bush. 16.1. Introduction -- 17. Control for discrete models of buildings including elastoplastic terms. 17.1. Introduction. 17.2. Reminder about Prandtl rheological model. 17.3. The studied models with n DOF. 17.4. Existence and uniqueness results. 17.5. Numerical scheme. 17.6. Control procedure. 17.7. Algorithm of control. 17.8 Numerical results for a system with 3 DOF. 17.9. Extension to nonlinear cases. 17.10. Conclusion.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical and computational developments.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Bifurcation theory.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85013940</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Chaotic behavior in systems.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85022562</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Differential equations, Nonlinear.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85037906</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Théorie de la bifurcation.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Chaos.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Équations différentielles non linéaires.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Differential Equations</subfield><subfield code="x">General.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Bifurcation theory</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Chaotic behavior in systems</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Differential equations, Nonlinear</subfield><subfield code="2">fast</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Lamarque, Claude-Henri.</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjCjcGqWkGPkqKytFJWMT3</subfield><subfield code="0">http://id.loc.gov/authorities/names/nr2003036751</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Bifurcation and chaos in nonsmooth mechanical systems (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCGj9ybF3Dyx4RtYJ3xpVRX</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Awrejcewicz, J. (Jan).</subfield><subfield code="t">Bifurcation and chaos in nonsmooth mechanical systems.</subfield><subfield code="d">Singapore ; River Edge, NJ : World Scientific, 2003</subfield><subfield code="z">9812384596</subfield><subfield code="w">(OCoLC)53362322</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">World Scientific series on nonlinear science.</subfield><subfield code="n">Series A,</subfield><subfield code="p">Monographs and treatises ;</subfield><subfield code="v">v. 45.</subfield><subfield code="0">http://id.loc.gov/authorities/names/no94008495</subfield></datafield><datafield tag="856" ind1="1" ind2=" "><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=135170</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="1" ind2=" "><subfield code="l">CBO01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=135170</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH21190640</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest Ebook Central</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL234346</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">135170</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">2407672</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocm61048703 |
| illustrated | Illustrated |
| indexdate | 2024-10-25T16:16:14Z |
| institution | BVB |
| isbn | 9812564802 9789812564801 |
| language | English |
| oclc_num | 61048703 |
| open_access_boolean | |
| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource (xvii, 543 pages :) |
| psigel | ZDB-4-EBA |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | World Scientific, |
| record_format | marc |
| series | World Scientific series on nonlinear science. Monographs and treatises ; |
| series2 | World Scientific series on nonlinear science. Series A, Monographs and treatises ; |
| spelling | Awrejcewicz, J. (Jan) https://id.oclc.org/worldcat/entity/E39PBJr83fkjVcwR6tgHmDBHG3 http://id.loc.gov/authorities/names/n88212452 Bifurcation and chaos in nonsmooth mechanical systems / Jan Awrejcewicz, Claude-Henri Lamarque. Singapore ; River Edge, NJ : World Scientific, 2003. 1 online resource (xvii, 543 pages :) text txt rdacontent computer c rdamedia online resource cr rdacarrier World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 45 Includes bibliographical references (pages 507-530) and index. Print version record. 1. Introduction to discontinuous ODEs. 1.1. Introduction. 1.2. Filippov's theory. 1.3. Aizerman's theory. 1.4. Examples. 1.5. Boundary value problem -- 2. Mathematical background for multivalued formulations. 2.1. Origin of nonlinearities. 2.2. Smooth and nonsmooth nonlinearities. 2.3. Examples and dynamical equilibria. 2.4. Existence and uniqueness. 2.5. Stochastic frame -- 3. Numerical schemes and analytical methods. 3.1. Numerical schemes. 3.2. Analytical methods -- 4. Properties of numerical schemes. 4.1. Dynamics of systems with friction or elastoplastic terms. 4.2. Systems with impacts. 4.3. Conclusion -- 5. Bifurcations of a particular van der Pol-Duffing oscillator. 5.1. The analysed system and the averaged equations. 5.2. "0" type bifurcations. 5.3. Complex bifurcations. 5.4. Observations of strange attractors using numerical simulations -- 6. Stick-slip oscillator with two degrees of freedom. 6.1. Introduction. 6.2. Disc -- flexible arm oscillator. 6.3. Two horizontally situated masses -- 7. Piecewise linear approximations. 7.1. Introduction. 7.2. Exact and approximated models. 7.3. Approximation and global dynamic behavior. 7.4. Numerical results. 7.5. Conclusion -- 8. Chua's circuit with discontinuities. 8.1. Introduction. 8.2. Mechanical realizations of Chua's circuit. 8.3. Generalized double scroll Chua's circuit -- 9. Mechanical system with impacts and modal approaches. 9.1. Introduction. 9.2. Single degree of freedom system. 9.3. Two degrees of freedom systems. 9.4. Conclusion -- 10. One DOF mechanical system with friction. 10.1. Introduction. 10.2. Modelling the pendulum with friction. 10.3. Numerical results. 10.4. The Melnikov analysis. 10.5. Conclusion. 11. Modelling the dynamical behaviour of elasto-plastic systems. 11.1. Rheological systems with "friction" -- 12. A mechanical system with 7 DOF. 12.1. Mathematical model. 12.2. Numerical results and comments for finite k3 -- 13. Stability of singular periodic motions in single degree of freedom vibro-impact oscillators and grazing bifurcations. 13.1. Introduction. 13.2. Mechanical system and change of coordinates. 13.3. Local expansion of the Poincaré map. 13.4. Stability of the nondifferentiable fixed point. 13.5. Applications. 13.6. Conclusion -- 14. Triple pendulum with impacts. 14.1. Introduction. 14.2. Investigated pendulum and governing equations (without impacts). 14.3. Introduction of the obstacles. 14.4. Calculation of the fundamental solution matrices for dynamical systems with impacts. 14.5. Simplification of the system. 14.6. The method used for integration of the system and its accuracy. 14.7. Numerical examples. 14.8. Concluding remarks -- 15. Analytical prediction of stick-slip chaos. 15.1. Introduction. 15.2. The Melnikov's method. 15.3. Analyzed system. 15.4. Analytical results -- 16. Thermoelasticity, wear and stick-slip movements of a rotating shaft with a rigid bush. 16.1. Introduction -- 17. Control for discrete models of buildings including elastoplastic terms. 17.1. Introduction. 17.2. Reminder about Prandtl rheological model. 17.3. The studied models with n DOF. 17.4. Existence and uniqueness results. 17.5. Numerical scheme. 17.6. Control procedure. 17.7. Algorithm of control. 17.8 Numerical results for a system with 3 DOF. 17.9. Extension to nonlinear cases. 17.10. Conclusion. This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical and computational developments. Bifurcation theory. http://id.loc.gov/authorities/subjects/sh85013940 Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Differential equations, Nonlinear. http://id.loc.gov/authorities/subjects/sh85037906 Théorie de la bifurcation. Chaos. Équations différentielles non linéaires. MATHEMATICS Differential Equations General. bisacsh Bifurcation theory fast Chaotic behavior in systems fast Differential equations, Nonlinear fast Lamarque, Claude-Henri. https://id.oclc.org/worldcat/entity/E39PCjCjcGqWkGPkqKytFJWMT3 http://id.loc.gov/authorities/names/nr2003036751 has work: Bifurcation and chaos in nonsmooth mechanical systems (Text) https://id.oclc.org/worldcat/entity/E39PCGj9ybF3Dyx4RtYJ3xpVRX https://id.oclc.org/worldcat/ontology/hasWork Print version: Awrejcewicz, J. (Jan). Bifurcation and chaos in nonsmooth mechanical systems. Singapore ; River Edge, NJ : World Scientific, 2003 9812384596 (OCoLC)53362322 World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 45. http://id.loc.gov/authorities/names/no94008495 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=135170 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=135170 Volltext |
| spellingShingle | Awrejcewicz, J. (Jan) Bifurcation and chaos in nonsmooth mechanical systems / World Scientific series on nonlinear science. Monographs and treatises ; 1. Introduction to discontinuous ODEs. 1.1. Introduction. 1.2. Filippov's theory. 1.3. Aizerman's theory. 1.4. Examples. 1.5. Boundary value problem -- 2. Mathematical background for multivalued formulations. 2.1. Origin of nonlinearities. 2.2. Smooth and nonsmooth nonlinearities. 2.3. Examples and dynamical equilibria. 2.4. Existence and uniqueness. 2.5. Stochastic frame -- 3. Numerical schemes and analytical methods. 3.1. Numerical schemes. 3.2. Analytical methods -- 4. Properties of numerical schemes. 4.1. Dynamics of systems with friction or elastoplastic terms. 4.2. Systems with impacts. 4.3. Conclusion -- 5. Bifurcations of a particular van der Pol-Duffing oscillator. 5.1. The analysed system and the averaged equations. 5.2. "0" type bifurcations. 5.3. Complex bifurcations. 5.4. Observations of strange attractors using numerical simulations -- 6. Stick-slip oscillator with two degrees of freedom. 6.1. Introduction. 6.2. Disc -- flexible arm oscillator. 6.3. Two horizontally situated masses -- 7. Piecewise linear approximations. 7.1. Introduction. 7.2. Exact and approximated models. 7.3. Approximation and global dynamic behavior. 7.4. Numerical results. 7.5. Conclusion -- 8. Chua's circuit with discontinuities. 8.1. Introduction. 8.2. Mechanical realizations of Chua's circuit. 8.3. Generalized double scroll Chua's circuit -- 9. Mechanical system with impacts and modal approaches. 9.1. Introduction. 9.2. Single degree of freedom system. 9.3. Two degrees of freedom systems. 9.4. Conclusion -- 10. One DOF mechanical system with friction. 10.1. Introduction. 10.2. Modelling the pendulum with friction. 10.3. Numerical results. 10.4. The Melnikov analysis. 10.5. Conclusion. 11. Modelling the dynamical behaviour of elasto-plastic systems. 11.1. Rheological systems with "friction" -- 12. A mechanical system with 7 DOF. 12.1. Mathematical model. 12.2. Numerical results and comments for finite k3 -- 13. Stability of singular periodic motions in single degree of freedom vibro-impact oscillators and grazing bifurcations. 13.1. Introduction. 13.2. Mechanical system and change of coordinates. 13.3. Local expansion of the Poincaré map. 13.4. Stability of the nondifferentiable fixed point. 13.5. Applications. 13.6. Conclusion -- 14. Triple pendulum with impacts. 14.1. Introduction. 14.2. Investigated pendulum and governing equations (without impacts). 14.3. Introduction of the obstacles. 14.4. Calculation of the fundamental solution matrices for dynamical systems with impacts. 14.5. Simplification of the system. 14.6. The method used for integration of the system and its accuracy. 14.7. Numerical examples. 14.8. Concluding remarks -- 15. Analytical prediction of stick-slip chaos. 15.1. Introduction. 15.2. The Melnikov's method. 15.3. Analyzed system. 15.4. Analytical results -- 16. Thermoelasticity, wear and stick-slip movements of a rotating shaft with a rigid bush. 16.1. Introduction -- 17. Control for discrete models of buildings including elastoplastic terms. 17.1. Introduction. 17.2. Reminder about Prandtl rheological model. 17.3. The studied models with n DOF. 17.4. Existence and uniqueness results. 17.5. Numerical scheme. 17.6. Control procedure. 17.7. Algorithm of control. 17.8 Numerical results for a system with 3 DOF. 17.9. Extension to nonlinear cases. 17.10. Conclusion. Bifurcation theory. http://id.loc.gov/authorities/subjects/sh85013940 Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Differential equations, Nonlinear. http://id.loc.gov/authorities/subjects/sh85037906 Théorie de la bifurcation. Chaos. Équations différentielles non linéaires. MATHEMATICS Differential Equations General. bisacsh Bifurcation theory fast Chaotic behavior in systems fast Differential equations, Nonlinear fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85013940 http://id.loc.gov/authorities/subjects/sh85022562 http://id.loc.gov/authorities/subjects/sh85037906 |
| title | Bifurcation and chaos in nonsmooth mechanical systems / |
| title_auth | Bifurcation and chaos in nonsmooth mechanical systems / |
| title_exact_search | Bifurcation and chaos in nonsmooth mechanical systems / |
| title_full | Bifurcation and chaos in nonsmooth mechanical systems / Jan Awrejcewicz, Claude-Henri Lamarque. |
| title_fullStr | Bifurcation and chaos in nonsmooth mechanical systems / Jan Awrejcewicz, Claude-Henri Lamarque. |
| title_full_unstemmed | Bifurcation and chaos in nonsmooth mechanical systems / Jan Awrejcewicz, Claude-Henri Lamarque. |
| title_short | Bifurcation and chaos in nonsmooth mechanical systems / |
| title_sort | bifurcation and chaos in nonsmooth mechanical systems |
| topic | Bifurcation theory. http://id.loc.gov/authorities/subjects/sh85013940 Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Differential equations, Nonlinear. http://id.loc.gov/authorities/subjects/sh85037906 Théorie de la bifurcation. Chaos. Équations différentielles non linéaires. MATHEMATICS Differential Equations General. bisacsh Bifurcation theory fast Chaotic behavior in systems fast Differential equations, Nonlinear fast |
| topic_facet | Bifurcation theory. Chaotic behavior in systems. Differential equations, Nonlinear. Théorie de la bifurcation. Chaos. Équations différentielles non linéaires. MATHEMATICS Differential Equations General. Bifurcation theory Chaotic behavior in systems Differential equations, Nonlinear |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=135170 |
| work_keys_str_mv | AT awrejcewiczj bifurcationandchaosinnonsmoothmechanicalsystems AT lamarqueclaudehenri bifurcationandchaosinnonsmoothmechanicalsystems |