Nonlinear Dynamics: Between Linear and Impact Limits
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2010
|
| Series: | Lecture Notes in Applied and Computational Mechanics
52 |
| Subjects: | |
| Online Access: | BTU01 FHI01 FHN01 FHR01 Volltext |
| Item Description: | Nonlinear Dynamics represents a wide interdisciplinary area of research dealing with a variety of "unusual" physical phenomena by means of nonlinear differential equations, discrete mappings, and related mathematical algorithms. However, with no real substitute for the linear superposition principle, the methods of Nonlinear Dynamics appeared to be very diverse, individual and technically complicated. This book makes an attempt to find a common ground for nonlinear dynamic analyses based on the existence of strongly nonlinear but quite simple counterparts to the linear models and tools. It is shown that, since the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, then translations and reflections, impact oscillators, and hyperbolic (Clifford’s) algebras must give rise to some "quasi impact" methodology. Such strongly nonlinear methods are developed in several chapters of this book based on the idea of non-smooth time substitutions. Although most of the illustrations are based on mechanical oscillators, the area of applications may include also electric, electro-mechanical, electrochemical and other physical models generating strongly anharmonic temporal signals or spatial distributions. Possible applications to periodic elastic structures with non-smooth or discontinuous characteristics are outlined in the final chapter of the book |
| Physical Description: | 1 Online-Ressource (360p) |
| ISBN: | 9783642127991 |
| DOI: | 10.1007/978-3-642-12799-1 |
Staff View
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV041889723 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 140603s2010 |||| o||u| ||||||eng d | ||
| 020 | |a 9783642127991 |c Online |9 978-3-642-12799-1 | ||
| 024 | 7 | |a 10.1007/978-3-642-12799-1 |2 doi | |
| 035 | |a (OCoLC)700000457 | ||
| 035 | |a (DE-599)BVBBV041889723 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-634 |a DE-898 |a DE-573 |a DE-92 |a DE-83 | ||
| 082 | 0 | |a 620 |2 23 | |
| 084 | |a SK 955 |0 (DE-625)143274: |2 rvk | ||
| 100 | 1 | |a Pilipchuk, Valery N. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonlinear Dynamics |b Between Linear and Impact Limits |c by Valery N. Pilipchuk |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 2010 | |
| 300 | |a 1 Online-Ressource (360p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Lecture Notes in Applied and Computational Mechanics |v 52 | |
| 500 | |a Nonlinear Dynamics represents a wide interdisciplinary area of research dealing with a variety of "unusual" physical phenomena by means of nonlinear differential equations, discrete mappings, and related mathematical algorithms. However, with no real substitute for the linear superposition principle, the methods of Nonlinear Dynamics appeared to be very diverse, individual and technically complicated. This book makes an attempt to find a common ground for nonlinear dynamic analyses based on the existence of strongly nonlinear but quite simple counterparts to the linear models and tools. It is shown that, since the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, then translations and reflections, impact oscillators, and hyperbolic (Clifford’s) algebras must give rise to some "quasi impact" methodology. Such strongly nonlinear methods are developed in several chapters of this book based on the idea of non-smooth time substitutions. Although most of the illustrations are based on mechanical oscillators, the area of applications may include also electric, electro-mechanical, electrochemical and other physical models generating strongly anharmonic temporal signals or spatial distributions. Possible applications to periodic elastic structures with non-smooth or discontinuous characteristics are outlined in the final chapter of the book | ||
| 505 | 0 | |a Smooth Oscillating Processes -- Nonsmooth Processes as Asymptotic Limits -- Nonsmooth Temporal Transformations (NSTT) -- Sawtooth Power Series -- NSTT for Linear and Piecewise-Linear Systems -- Periodic and Transient Nonlinear Dynamics under Discontinuous Loading -- Strongly Nonlinear Vibrations -- Strongly Nonlinear Waves -- Impact Modes and Parameter Variations -- Principal Trajectories of Forced Vibrations -- NSTT and Shooting Method for Periodic Motions -- Essentially Non-periodic Processes -- Spatially-Oscillating Structures | |
| 650 | 4 | |a Engineering | |
| 650 | 4 | |a Physics | |
| 650 | 4 | |a Mechanics | |
| 650 | 4 | |a Vibration | |
| 650 | 4 | |a Vibration, Dynamical Systems, Control | |
| 650 | 4 | |a Complexity | |
| 650 | 4 | |a Ingenieurwissenschaften | |
| 650 | 0 | 7 | |a Nichtlineare Dynamik |0 (DE-588)4126141-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare Dynamik |0 (DE-588)4126141-0 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-3-642-12798-4 |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-642-12799-1 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-ENG | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027333677 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u https://doi.org/10.1007/978-3-642-12799-1 |l BTU01 |p ZDB-2-ENG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1007/978-3-642-12799-1 |l FHI01 |p ZDB-2-ENG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1007/978-3-642-12799-1 |l FHN01 |p ZDB-2-ENG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1007/978-3-642-12799-1 |l FHR01 |p ZDB-2-ENG |x Verlag |3 Volltext | |
Record in the Search Index
| _version_ | 1804152238944288768 |
|---|---|
| any_adam_object | |
| author | Pilipchuk, Valery N. |
| author_facet | Pilipchuk, Valery N. |
| author_role | aut |
| author_sort | Pilipchuk, Valery N. |
| author_variant | v n p vn vnp |
| building | Verbundindex |
| bvnumber | BV041889723 |
| classification_rvk | SK 955 |
| collection | ZDB-2-ENG |
| contents | Smooth Oscillating Processes -- Nonsmooth Processes as Asymptotic Limits -- Nonsmooth Temporal Transformations (NSTT) -- Sawtooth Power Series -- NSTT for Linear and Piecewise-Linear Systems -- Periodic and Transient Nonlinear Dynamics under Discontinuous Loading -- Strongly Nonlinear Vibrations -- Strongly Nonlinear Waves -- Impact Modes and Parameter Variations -- Principal Trajectories of Forced Vibrations -- NSTT and Shooting Method for Periodic Motions -- Essentially Non-periodic Processes -- Spatially-Oscillating Structures |
| ctrlnum | (OCoLC)700000457 (DE-599)BVBBV041889723 |
| dewey-full | 620 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620 |
| dewey-search | 620 |
| dewey-sort | 3620 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-12799-1 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04025nmm a2200541zcb4500</leader><controlfield tag="001">BV041889723</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">140603s2010 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642127991</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-642-12799-1</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-642-12799-1</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)700000457</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV041889723</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-634</subfield><subfield code="a">DE-898</subfield><subfield code="a">DE-573</subfield><subfield code="a">DE-92</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">620</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 955</subfield><subfield code="0">(DE-625)143274:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Pilipchuk, Valery N.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Nonlinear Dynamics</subfield><subfield code="b">Between Linear and Impact Limits</subfield><subfield code="c">by Valery N. Pilipchuk</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin, Heidelberg</subfield><subfield code="b">Springer Berlin Heidelberg</subfield><subfield code="c">2010</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (360p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Lecture Notes in Applied and Computational Mechanics</subfield><subfield code="v">52</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Nonlinear Dynamics represents a wide interdisciplinary area of research dealing with a variety of "unusual" physical phenomena by means of nonlinear differential equations, discrete mappings, and related mathematical algorithms. However, with no real substitute for the linear superposition principle, the methods of Nonlinear Dynamics appeared to be very diverse, individual and technically complicated. This book makes an attempt to find a common ground for nonlinear dynamic analyses based on the existence of strongly nonlinear but quite simple counterparts to the linear models and tools. It is shown that, since the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, then translations and reflections, impact oscillators, and hyperbolic (Clifford’s) algebras must give rise to some "quasi impact" methodology. Such strongly nonlinear methods are developed in several chapters of this book based on the idea of non-smooth time substitutions. Although most of the illustrations are based on mechanical oscillators, the area of applications may include also electric, electro-mechanical, electrochemical and other physical models generating strongly anharmonic temporal signals or spatial distributions. Possible applications to periodic elastic structures with non-smooth or discontinuous characteristics are outlined in the final chapter of the book</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Smooth Oscillating Processes -- Nonsmooth Processes as Asymptotic Limits -- Nonsmooth Temporal Transformations (NSTT) -- Sawtooth Power Series -- NSTT for Linear and Piecewise-Linear Systems -- Periodic and Transient Nonlinear Dynamics under Discontinuous Loading -- Strongly Nonlinear Vibrations -- Strongly Nonlinear Waves -- Impact Modes and Parameter Variations -- Principal Trajectories of Forced Vibrations -- NSTT and Shooting Method for Periodic Motions -- Essentially Non-periodic Processes -- Spatially-Oscillating Structures</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Engineering</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Physics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mechanics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Vibration</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Vibration, Dynamical Systems, Control</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Complexity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Ingenieurwissenschaften</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineare Dynamik</subfield><subfield code="0">(DE-588)4126141-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtlineare Dynamik</subfield><subfield code="0">(DE-588)4126141-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">978-3-642-12798-4</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-642-12799-1</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-ENG</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027333677</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/978-3-642-12799-1</subfield><subfield code="l">BTU01</subfield><subfield code="p">ZDB-2-ENG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/978-3-642-12799-1</subfield><subfield code="l">FHI01</subfield><subfield code="p">ZDB-2-ENG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/978-3-642-12799-1</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-2-ENG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/978-3-642-12799-1</subfield><subfield code="l">FHR01</subfield><subfield code="p">ZDB-2-ENG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV041889723 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:07:33Z |
| institution | BVB |
| isbn | 9783642127991 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027333677 |
| oclc_num | 700000457 |
| open_access_boolean | |
| owner | DE-634 DE-898 DE-BY-UBR DE-573 DE-92 DE-83 |
| owner_facet | DE-634 DE-898 DE-BY-UBR DE-573 DE-92 DE-83 |
| physical | 1 Online-Ressource (360p) |
| psigel | ZDB-2-ENG |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Lecture Notes in Applied and Computational Mechanics |
| spelling | Pilipchuk, Valery N. Verfasser aut Nonlinear Dynamics Between Linear and Impact Limits by Valery N. Pilipchuk Berlin, Heidelberg Springer Berlin Heidelberg 2010 1 Online-Ressource (360p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Applied and Computational Mechanics 52 Nonlinear Dynamics represents a wide interdisciplinary area of research dealing with a variety of "unusual" physical phenomena by means of nonlinear differential equations, discrete mappings, and related mathematical algorithms. However, with no real substitute for the linear superposition principle, the methods of Nonlinear Dynamics appeared to be very diverse, individual and technically complicated. This book makes an attempt to find a common ground for nonlinear dynamic analyses based on the existence of strongly nonlinear but quite simple counterparts to the linear models and tools. It is shown that, since the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, then translations and reflections, impact oscillators, and hyperbolic (Clifford’s) algebras must give rise to some "quasi impact" methodology. Such strongly nonlinear methods are developed in several chapters of this book based on the idea of non-smooth time substitutions. Although most of the illustrations are based on mechanical oscillators, the area of applications may include also electric, electro-mechanical, electrochemical and other physical models generating strongly anharmonic temporal signals or spatial distributions. Possible applications to periodic elastic structures with non-smooth or discontinuous characteristics are outlined in the final chapter of the book Smooth Oscillating Processes -- Nonsmooth Processes as Asymptotic Limits -- Nonsmooth Temporal Transformations (NSTT) -- Sawtooth Power Series -- NSTT for Linear and Piecewise-Linear Systems -- Periodic and Transient Nonlinear Dynamics under Discontinuous Loading -- Strongly Nonlinear Vibrations -- Strongly Nonlinear Waves -- Impact Modes and Parameter Variations -- Principal Trajectories of Forced Vibrations -- NSTT and Shooting Method for Periodic Motions -- Essentially Non-periodic Processes -- Spatially-Oscillating Structures Engineering Physics Mechanics Vibration Vibration, Dynamical Systems, Control Complexity Ingenieurwissenschaften Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 s 1\p DE-604 Erscheint auch als Druckausgabe 978-3-642-12798-4 https://doi.org/10.1007/978-3-642-12799-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pilipchuk, Valery N. Nonlinear Dynamics Between Linear and Impact Limits Smooth Oscillating Processes -- Nonsmooth Processes as Asymptotic Limits -- Nonsmooth Temporal Transformations (NSTT) -- Sawtooth Power Series -- NSTT for Linear and Piecewise-Linear Systems -- Periodic and Transient Nonlinear Dynamics under Discontinuous Loading -- Strongly Nonlinear Vibrations -- Strongly Nonlinear Waves -- Impact Modes and Parameter Variations -- Principal Trajectories of Forced Vibrations -- NSTT and Shooting Method for Periodic Motions -- Essentially Non-periodic Processes -- Spatially-Oscillating Structures Engineering Physics Mechanics Vibration Vibration, Dynamical Systems, Control Complexity Ingenieurwissenschaften Nichtlineare Dynamik (DE-588)4126141-0 gnd |
| subject_GND | (DE-588)4126141-0 |
| title | Nonlinear Dynamics Between Linear and Impact Limits |
| title_auth | Nonlinear Dynamics Between Linear and Impact Limits |
| title_exact_search | Nonlinear Dynamics Between Linear and Impact Limits |
| title_full | Nonlinear Dynamics Between Linear and Impact Limits by Valery N. Pilipchuk |
| title_fullStr | Nonlinear Dynamics Between Linear and Impact Limits by Valery N. Pilipchuk |
| title_full_unstemmed | Nonlinear Dynamics Between Linear and Impact Limits by Valery N. Pilipchuk |
| title_short | Nonlinear Dynamics |
| title_sort | nonlinear dynamics between linear and impact limits |
| title_sub | Between Linear and Impact Limits |
| topic | Engineering Physics Mechanics Vibration Vibration, Dynamical Systems, Control Complexity Ingenieurwissenschaften Nichtlineare Dynamik (DE-588)4126141-0 gnd |
| topic_facet | Engineering Physics Mechanics Vibration Vibration, Dynamical Systems, Control Complexity Ingenieurwissenschaften Nichtlineare Dynamik |
| url | https://doi.org/10.1007/978-3-642-12799-1 |
| work_keys_str_mv | AT pilipchukvaleryn nonlineardynamicsbetweenlinearandimpactlimits |