Unlike most other such texts which emphasize particular methods, this text synthesizes analytical, experimental, and numerical methods, providing a unified treatment of nonlinear dynamics. It presents mathematical concepts in a manner comprehensible to engineers and applied scientists. Includes many exercises and worked-out examples and an extensive bibliography. Annotation copyright Book News, Inc. Portland, Or.
A unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincar? maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to facilitate understanding.
| Preface |
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xiii | |
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1 | (34) |
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2 | (4) |
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6 | (9) |
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6 | (5) |
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11 | (2) |
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Phase Portraits and Flows |
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13 | (2) |
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15 | (5) |
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20 | (9) |
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20 | (3) |
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23 | (2) |
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25 | (2) |
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Lagrange Stability (Bounded Stability) |
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27 | (1) |
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Stability Through Lyapunov Function |
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27 | (2) |
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29 | (2) |
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31 | (1) |
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31 | (4) |
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35 | (112) |
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35 | (26) |
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Linearization Near an Equilibrium Solution |
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36 | (3) |
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Classification and Stability of Equilibrium Solutions |
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39 | (8) |
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Eigenspaces and Invariant Manifolds |
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47 | (11) |
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Analytical Construction of Stable and Unstable Manifolds |
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58 | (3) |
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61 | (7) |
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Bifurcations of Continuous Systems |
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68 | (53) |
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Local Bifurcations of Fixed Points |
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70 | (11) |
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Normal Forms for Bifurcations |
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81 | (2) |
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Bifurcation Diagrams and Sets |
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83 | (13) |
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Center Manifold Reduction |
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96 | (12) |
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The Lyapunov-Schmidt Method |
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108 | (1) |
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The Method of Multiple Scales |
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108 | (7) |
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115 | (1) |
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Stability of Bifurcations to Perturbations |
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116 | (3) |
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Codimension of a Bifurcation |
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119 | (2) |
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121 | (1) |
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121 | (7) |
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128 | (19) |
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147 | (84) |
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147 | (11) |
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148 | (8) |
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156 | (2) |
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158 | (1) |
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158 | (14) |
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159 | (10) |
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169 | (2) |
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Comments on the Monodromy Matrix |
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171 | (1) |
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Manifolds of a Periodic Solution |
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172 | (1) |
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172 | (15) |
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176 | (5) |
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181 | (6) |
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187 | (21) |
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Symmetry--Breaking Bifurcation |
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189 | (6) |
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195 | (5) |
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Period--Doubling or Flip Bifurcation |
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200 | (4) |
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Transcritical Bifurcation |
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204 | (1) |
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Secondary Hopf or Neimark Bifurcation |
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205 | (3) |
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208 | (11) |
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Method of Multiple Scales |
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209 | (3) |
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Center Manifold Reduction |
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212 | (5) |
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217 | (2) |
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219 | (12) |
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231 | (46) |
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233 | (9) |
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Winding Time and Rotation Number |
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238 | (2) |
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Second-Order Poincare Map |
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240 | (1) |
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241 | (1) |
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242 | (6) |
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248 | (6) |
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Method of Multiple Scales |
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249 | (2) |
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251 | (2) |
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253 | (1) |
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254 | (1) |
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255 | (14) |
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269 | (8) |
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277 | (146) |
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278 | (10) |
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288 | (7) |
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295 | (1) |
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296 | (18) |
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300 | (5) |
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305 | (6) |
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311 | (3) |
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314 | (20) |
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315 | (2) |
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317 | (14) |
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331 | (3) |
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334 | (22) |
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356 | (34) |
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356 | (3) |
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359 | (4) |
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Numerical Prediction of Manifold Intersections |
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363 | (3) |
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Analytical Prediction of Manifold Intersections |
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366 | (8) |
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Application of Melnikov's Method |
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374 | (16) |
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390 | (1) |
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Bifurcations of Homoclinic Orbits |
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390 | (20) |
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391 | (6) |
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Orbits Homoclinic to a Saddle |
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397 | (5) |
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Orbits Homoclinic to a Saddle Focus |
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402 | (5) |
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407 | (3) |
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410 | (13) |
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423 | (38) |
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Continuation of Fixed Points |
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423 | (13) |
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425 | (3) |
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Davidenko-Newton-Raphson Continuation |
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428 | (1) |
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428 | (4) |
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Pseudo-Arclength Continuation |
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432 | (3) |
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435 | (1) |
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Simple Turning and Branch Points |
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436 | (2) |
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438 | (3) |
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441 | (4) |
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Construction of Periodic Solutions |
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445 | (10) |
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446 | (3) |
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449 | (6) |
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455 | (1) |
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Continuation of Periodic Solutions |
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455 | (6) |
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456 | (1) |
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456 | (2) |
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Pseudo-Arclength Continuation |
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458 | (2) |
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460 | (1) |
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461 | (102) |
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462 | (3) |
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465 | (7) |
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472 | (6) |
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478 | (24) |
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Choosing the Embedding Dimension |
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483 | (12) |
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495 | (5) |
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Two or More Measured Signals |
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500 | (2) |
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502 | (12) |
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Poincare Sections and Maps |
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514 | (6) |
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514 | (2) |
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516 | (3) |
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Higher-Order Poincare Sections |
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519 | (1) |
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519 | (1) |
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Autocorrelation Functions |
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520 | (5) |
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525 | (13) |
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Concept of Lyapunov Exponents |
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525 | (4) |
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529 | (2) |
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531 | (3) |
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534 | (3) |
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537 | (1) |
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538 | (12) |
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538 | (3) |
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541 | (4) |
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545 | (2) |
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547 | (1) |
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Generalized Correlation Dimension |
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548 | (1) |
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549 | (1) |
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549 | (1) |
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550 | (7) |
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557 | (6) |
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563 | (26) |
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563 | (8) |
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564 | (4) |
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568 | (3) |
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571 | (1) |
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571 | (13) |
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572 | (5) |
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Implementation of the OGY Scheme |
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577 | (3) |
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580 | (2) |
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Traditional Control Methods |
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582 | (2) |
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584 | (5) |
| Bibliography |
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589 | (74) |
| Subject Index |
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663 | |
Ali H. Nayfeh is a University Distinguished Professor of Engineering Science and Mechanics at the Virginia Polytechnic Institute and State University, Blacksburg, Virginia. Professor Nayfeh is the Editor-in-Chief of the journal Nonlinear Dynamics and the Journal of Vibration and Control. He is the author of Perturbation Methods (Wiley, 1973), Nonlinear Oscillations (coauthored with Dean T. Mook; Wiley,1979), Introduction to Perturbation techniques (Wiley, 1981), Problems in Perturbation (Wiley, 1985), and Method of Normal Forms (Wiley, 1993). Professor Nayfeh's areas of interest include nonlinear vibrations and dynamics, wave propagation, ship and submarine motions, structural dynamics, acoustics, aerodynamic/dynamic/structure/control interactions, flight mechanics, and transition from laminar to turbulent flows.
Balakumar Balachandran is Assistant Professor of Mechanical Engineering at the University of Maryland, College Park, Maryland. His areas of interest include vibration and acoustics control, nonlinear dynamics, structural dynamics, and system identification.
Lisainfo e-raamatute kohta