Averaging methods in nonlinear dynamical systems:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2007
|
| Ausgabe: | second edition |
| Schriftenreihe: | Applied mathematical sciences
59 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | xxi, 431 Seiten |
| ISBN: | 9780387489162 0387489169 9781441923769 |
Internformat
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| 100 | 1 | |a Sanders, Jan A. |0 (DE-588)127872379X |4 aut | |
| 245 | 1 | 0 | |a Averaging methods in nonlinear dynamical systems |c J. A. Sanders ; F. Verhulst ; J. Murdock |
| 250 | |a second edition | ||
| 264 | 1 | |a New York, NY |b Springer |c 2007 | |
| 300 | |a xxi, 431 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applied mathematical sciences |v 59 | |
| 650 | 4 | |a Averaging method (Differential equations) | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Differential equations, Nonlinear |x Numerical solutions | |
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| 650 | 0 | 7 | |a Qualitative Theorie |0 (DE-588)4571165-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mittelungsverfahren |0 (DE-588)4126019-3 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1805088979434864640 |
|---|---|
| adam_text |
J.A. SANDERS F. VERHULST J. MURDOCK AVERAGING METHODS IN NONLINEAR
DYNAMICAL SYSTEMS SECOND EDITION 4Y SPRINGER LIST OF FIGURES 0.1 THE MAP
OF THE BOOK XXIII 2.1 PHASE ORBITS OF THE VAN DER POL EQUATION X + X =
E(L * X 2 )X . 23 2.2 SOLUTION X(T) OF X + X = ^X 2 COS(I), X(0) = 0,
X(0) = 1 26 2.3 EXACT AND APPROXIMATE SOLUTIONS OF X + X = EX 27 2.4
'CRUDE AVERAGING' OF X + 4ECOS 2 (T)I; + X = 0 28 2.5 PHASE PLANE FOR X
+ 4ECOS 2 (T)X + X = 0 29 2.6 PHASE PLANE OF THE EQUATION X + X ~ EX 2 =
E 2 (L * X 2 )X 42 4.1 F(T) = J2*=I SIN(T/2") AS A FUNCTION OF TIME 85
4.2 THE QUANTITY 5X/(EM) AS A FUNCTION OF 86 5.1 PHASE PLANE FOR THE
SYSTEM WITHOUT INTERACTION OF THE SPECIES. . 94 5.2 PHASE PLANE FOR THE
SYSTEM WITH INTERACTION OF THE SPECIES 95 5.3 RESPONSE CURVES FOR THE
HARMONICALLY FORCED DUFFING EQUATION. . 98 5.4 SOLUTION X STARTS IN X(0)
AND ATTRACTS TOWARDS 0 101 5.5 LINEAR ATTRACTION FOR THE EQUATION X + X
+ EX 3 + 3E 2 X = 0 110 6.1 CONNECTION DIAGRAM FOR TWO COUPLED DUFFING
EQUATIONS 116 6.2 SEPARATION OF NEARBY SOLUTIONS BY A HYPERBOLIC REST
POINT 121 6.3 A BOX NEIGHBORHOOD 124 6.4 A CONNECTING ORBIT 130 6.5 A
CONNECTING ORBIT 131 6.6 A DUMBBELL NEIGHBORHOOD 132 6.7 A SADDLE
CONNECTION IN THE PLANE 140 7.1 OSCILLATOR ATTACHED TO A FLYWHEEL 154
8.1 PHASE FLOW OF 4 + E/3{0) SIN(0) = EA(0) 173 8.2 SOLUTIONS X = X 2
(T) BASED ON EQUATION (8.5.2) 179 10.1 ONE NORMAL MODE PASSES THROUGH
THE CENTER OF THE SECOND ONE. . 219 LIST OF FIGURES 10.2 THE NORMAL
MODES ARE LINKED 219 10.3 POINCARE-MAP IN THE LINEAR CASE 219 10.4
BIFURCATION DIAGRAM FOR THE 1 : 2-RESONANCE 226 10.5 POINCARE SECTION
FOR THE EXACT 1 : 2-RESONANCE 226 10.6 PROJECTIONS FOR THE RESONANCES
4:1,4:3 AND 9:2 235 10.7 POINCARE MAP FOR THE 1 : 6-RESONANCE OF THE
ELASTIC PENDULUM. . . 236 10.8 ACTION SIMPLEX 242 10.9 ACTION SIMPLEX
FOR THE THE 1:2: 1-RESONANCE 251 10.10ACTION SIMPLEX FOR THE DISCRETE
SYMMETRIC 1:2: 1-RESONANCE. . . 252 LO.HACTION SIMPLEX FOR THE 1:2:
2-RESONANCE NORMALIZED TO H 1 253 10.12ACTION SIMPLEX FOR THE 1:2:
2-RESONANCE NORMALIZED TO H 2 254 10.13ACTION SIMPLEX FOR THE 1:2:
3-RESONANCE 256 10.14THE INVARIANT MANIFOLD EMBEDDED IN THE ENERGY
MANIFOLD 256 10.15ACTION SIMPLEX FOR THE 1:2: 4-RESONANCE FOR A 0 258
10.16ACTION SIMPLICES FOR THE 1:2: 5-RESONANCE 261 |
| adam_txt |
J.A. SANDERS F. VERHULST J. MURDOCK AVERAGING METHODS IN NONLINEAR
DYNAMICAL SYSTEMS SECOND EDITION 4Y SPRINGER LIST OF FIGURES 0.1 THE MAP
OF THE BOOK XXIII 2.1 PHASE ORBITS OF THE VAN DER POL EQUATION X + X =
E(L * X 2 )X . 23 2.2 SOLUTION X(T) OF X + X = ^X 2 COS(I), X(0) = 0,
X(0) = 1 26 2.3 EXACT AND APPROXIMATE SOLUTIONS OF X + X = EX 27 2.4
'CRUDE AVERAGING' OF X + 4ECOS 2 (T)I; + X = 0 28 2.5 PHASE PLANE FOR X
+ 4ECOS 2 (T)X + X = 0 29 2.6 PHASE PLANE OF THE EQUATION X + X ~ EX 2 =
E 2 (L * X 2 )X 42 4.1 F(T) = J2*=I SIN(T/2") AS A FUNCTION OF TIME 85
4.2 THE QUANTITY 5X/(EM) AS A FUNCTION OF 86 5.1 PHASE PLANE FOR THE
SYSTEM WITHOUT INTERACTION OF THE SPECIES. . 94 5.2 PHASE PLANE FOR THE
SYSTEM WITH INTERACTION OF THE SPECIES 95 5.3 RESPONSE CURVES FOR THE
HARMONICALLY FORCED DUFFING EQUATION. . 98 5.4 SOLUTION X STARTS IN X(0)
AND ATTRACTS TOWARDS 0 101 5.5 LINEAR ATTRACTION FOR THE EQUATION X + X
+ EX 3 + 3E 2 X = 0 110 6.1 CONNECTION DIAGRAM FOR TWO COUPLED DUFFING
EQUATIONS 116 6.2 SEPARATION OF NEARBY SOLUTIONS BY A HYPERBOLIC REST
POINT 121 6.3 A BOX NEIGHBORHOOD 124 6.4 A CONNECTING ORBIT 130 6.5 A
CONNECTING ORBIT 131 6.6 A DUMBBELL NEIGHBORHOOD 132 6.7 A SADDLE
CONNECTION IN THE PLANE 140 7.1 OSCILLATOR ATTACHED TO A FLYWHEEL 154
8.1 PHASE FLOW OF 4 + E/3{0) SIN(0) = EA(0) 173 8.2 SOLUTIONS X = X 2
(T) BASED ON EQUATION (8.5.2) 179 10.1 ONE NORMAL MODE PASSES THROUGH
THE CENTER OF THE SECOND ONE. . 219 LIST OF FIGURES 10.2 THE NORMAL
MODES ARE LINKED 219 10.3 POINCARE-MAP IN THE LINEAR CASE 219 10.4
BIFURCATION DIAGRAM FOR THE 1 : 2-RESONANCE 226 10.5 POINCARE SECTION
FOR THE EXACT 1 : 2-RESONANCE 226 10.6 PROJECTIONS FOR THE RESONANCES
4:1,4:3 AND 9:2 235 10.7 POINCARE MAP FOR THE 1 : 6-RESONANCE OF THE
ELASTIC PENDULUM. . . 236 10.8 ACTION SIMPLEX 242 10.9 ACTION SIMPLEX
FOR THE THE 1:2: 1-RESONANCE 251 10.10ACTION SIMPLEX FOR THE DISCRETE
SYMMETRIC 1:2: 1-RESONANCE. . . 252 LO.HACTION SIMPLEX FOR THE 1:2:
2-RESONANCE NORMALIZED TO H 1 253 10.12ACTION SIMPLEX FOR THE 1:2:
2-RESONANCE NORMALIZED TO H 2 254 10.13ACTION SIMPLEX FOR THE 1:2:
3-RESONANCE 256 10.14THE INVARIANT MANIFOLD EMBEDDED IN THE ENERGY
MANIFOLD 256 10.15ACTION SIMPLEX FOR THE 1:2: 4-RESONANCE FOR A 0 258
10.16ACTION SIMPLICES FOR THE 1:2: 5-RESONANCE 261 |
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| author | Sanders, Jan A. Verhulst, Ferdinand 1939- Murdock, James A. |
| author_GND | (DE-588)127872379X (DE-588)111117755 (DE-588)172268427 |
| author_facet | Sanders, Jan A. Verhulst, Ferdinand 1939- Murdock, James A. |
| author_role | aut aut aut |
| author_sort | Sanders, Jan A. |
| author_variant | j a s ja jas f v fv j a m ja jam |
| building | Verbundindex |
| bvnumber | BV022428482 |
| callnumber-first | Q - Science |
| callnumber-label | QA1 |
| callnumber-raw | QA1 QA372 |
| callnumber-search | QA1 QA372 |
| callnumber-sort | QA 11 |
| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)77012328 (DE-599)BVBBV022428482 |
| dewey-full | 515.355 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.355 |
| dewey-search | 515.355 |
| dewey-sort | 3515.355 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | second edition |
| format | Book |
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| id | DE-604.BV022428482 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T17:28:21Z |
| indexdate | 2024-07-20T09:16:37Z |
| institution | BVB |
| isbn | 9780387489162 0387489169 9781441923769 |
| language | English |
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| oclc_num | 77012328 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-634 DE-11 DE-29T DE-83 |
| owner_facet | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-634 DE-11 DE-29T DE-83 |
| physical | xxi, 431 Seiten |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Sanders, Jan A. (DE-588)127872379X aut Averaging methods in nonlinear dynamical systems J. A. Sanders ; F. Verhulst ; J. Murdock second edition New York, NY Springer 2007 xxi, 431 Seiten txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 59 Averaging method (Differential equations) Differentiable dynamical systems Differential equations, Nonlinear Numerical solutions Randwertproblem (DE-588)4048395-2 gnd rswk-swf Qualitative Theorie (DE-588)4571165-3 gnd rswk-swf Mittelungsverfahren (DE-588)4126019-3 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd rswk-swf Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 s Mittelungsverfahren (DE-588)4126019-3 s DE-604 Asymptotische Methode (DE-588)4287476-2 s Differenzierbares dynamisches System (DE-588)4137931-7 s Hyperbolische Differentialgleichung (DE-588)4131213-2 s Randwertproblem (DE-588)4048395-2 s Verzweigung Mathematik (DE-588)4078889-1 s Qualitative Theorie (DE-588)4571165-3 s Verhulst, Ferdinand 1939- (DE-588)111117755 aut Murdock, James A. (DE-588)172268427 aut Applied mathematical sciences 59 (DE-604)BV000005274 59 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2863108&prov=M&dok_var=1&dok_ext=htm Inhaltstext GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015636711&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sanders, Jan A. Verhulst, Ferdinand 1939- Murdock, James A. Averaging methods in nonlinear dynamical systems Applied mathematical sciences Averaging method (Differential equations) Differentiable dynamical systems Differential equations, Nonlinear Numerical solutions Randwertproblem (DE-588)4048395-2 gnd Qualitative Theorie (DE-588)4571165-3 gnd Mittelungsverfahren (DE-588)4126019-3 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Asymptotische Methode (DE-588)4287476-2 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4571165-3 (DE-588)4126019-3 (DE-588)4126142-2 (DE-588)4078889-1 (DE-588)4131213-2 (DE-588)4287476-2 (DE-588)4137931-7 |
| title | Averaging methods in nonlinear dynamical systems |
| title_auth | Averaging methods in nonlinear dynamical systems |
| title_exact_search | Averaging methods in nonlinear dynamical systems |
| title_exact_search_txtP | Averaging methods in nonlinear dynamical systems |
| title_full | Averaging methods in nonlinear dynamical systems J. A. Sanders ; F. Verhulst ; J. Murdock |
| title_fullStr | Averaging methods in nonlinear dynamical systems J. A. Sanders ; F. Verhulst ; J. Murdock |
| title_full_unstemmed | Averaging methods in nonlinear dynamical systems J. A. Sanders ; F. Verhulst ; J. Murdock |
| title_short | Averaging methods in nonlinear dynamical systems |
| title_sort | averaging methods in nonlinear dynamical systems |
| topic | Averaging method (Differential equations) Differentiable dynamical systems Differential equations, Nonlinear Numerical solutions Randwertproblem (DE-588)4048395-2 gnd Qualitative Theorie (DE-588)4571165-3 gnd Mittelungsverfahren (DE-588)4126019-3 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Asymptotische Methode (DE-588)4287476-2 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| topic_facet | Averaging method (Differential equations) Differentiable dynamical systems Differential equations, Nonlinear Numerical solutions Randwertproblem Qualitative Theorie Mittelungsverfahren Nichtlineares dynamisches System Verzweigung Mathematik Hyperbolische Differentialgleichung Asymptotische Methode Differenzierbares dynamisches System |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2863108&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015636711&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
| work_keys_str_mv | AT sandersjana averagingmethodsinnonlineardynamicalsystems AT verhulstferdinand averagingmethodsinnonlineardynamicalsystems AT murdockjamesa averagingmethodsinnonlineardynamicalsystems |