LEADER 05294nam 2200637Ia 450 001 9910130959903321 005 20170815160001.0 010 $a3-527-63577-7 010 $a1-283-92749-7 010 $a3-527-63578-5 010 $a3-527-63580-7 035 $a(CKB)3460000000080845 035 $a(EBL)822714 035 $a(OCoLC)797919122 035 $a(SSID)ssj0000622295 035 $a(PQKBManifestationID)11386143 035 $a(PQKBTitleCode)TC0000622295 035 $a(PQKBWorkID)10638259 035 $a(PQKB)11747298 035 $a(MiAaPQ)EBC822714 035 $a(EXLCZ)993460000000080845 100 $a20120112d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe method of normal forms$b[electronic resource] /$fAli Hasan Nayfeh 205 $a2nd, updated and enl. ed. 210 $aWeinheim, Germany $cWiley-VCH$dc2011 215 $a1 online resource (343 p.) 300 $aDescription based upon print version of record. 311 $a3-527-41097-X 320 $aIncludes bibliographical references and index. 327 $aThe Method of Normal Forms; Contents; Preface; Introduction; 1 SDOF Autonomous Systems; 1.1 Introduction; 1.2 Duffing Equation; 1.3 Rayleigh Equation; 1.4 Duffing-Rayleigh-van der Pol Equation; 1.5 An Oscillator with Quadratic and Cubic Nonlinearities; 1.5.1 Successive Transformations; 1.5.2 The Method of Multiple Scales; 1.5.3 A Single Transformation; 1.6 A General System with Quadratic and Cubic Nonlinearities; 1.7 The van der Pol Oscillator; 1.7.1 The Method of Normal Forms; 1.7.2 The Method of Multiple Scales; 1.8 Exercises; 2 Systems of First-Order Equations; 2.1 Introduction 327 $a2.2 A Two-Dimensional System with Diagonal Linear Part2.3 A Two-Dimensional System with a Nonsemisimple Linear Form; 2.4 An n-Dimensional System with Diagonal Linear Part; 2.5 A Two-Dimensional System with Purely Imaginary Eigenvalues; 2.5.1 The Method of Normal Forms; 2.5.2 The Method of Multiple Scales; 2.6 A Two-Dimensional System with Zero Eigenvalues; 2.7 A Three-Dimensional System with Zeroand Two Purely Imaginary Eigenvalues; 2.8 The Mathieu Equation; 2.9 Exercises; 3 Maps; 3.1 Linear Maps; 3.1.1 Case of Distinct Eigenvalues; 3.1.2 Case of Repeated Eigenvalues; 3.2 Nonlinear Maps 327 $a3.3 Center-Manifold Reduction3.4 Local Bifurcations; 3.4.1 Fold or Tangent or Saddle-Node Bifurcation; 3.4.2 Transcritical Bifurcation; 3.4.3 Pitchfork Bifurcation; 3.4.4 Flip or Period-Doubling Bifurcation; 3.4.5 Hopf or Neimark-Sacker Bifurcation; 3.5 Exercises; 4 Bifurcations of Continuous Systems; 4.1 Linear Systems; 4.1.1 Case of Distinct Eigenvalues; 4.1.2 Case of Repeated Eigenvalues; 4.2 Fixed Points of Nonlinear Systems; 4.2.1 Stability of Fixed Points; 4.2.2 Classification of Fixed Points; 4.2.3 Hartman-Grobman and Shoshitaishvili Theorems; 4.3 Center-Manifold Reduction 327 $a4.4 Local Bifurcations of Fixed Points4.4.1 Saddle-Node Bifurcation; 4.4.2 Nonbifurcation Point; 4.4.3 Transcritical Bifurcation; 4.4.4 Pitchfork Bifurcation; 4.4.5 Hopf Bifurcations; 4.5 Normal Forms of Static Bifurcations; 4.5.1 The Method of Multiple Scales; 4.5.2 Center-Manifold Reduction; 4.5.3 A Projection Method; 4.6 Normal Form of Hopf Bifurcation; 4.6.1 The Method of Multiple Scales; 4.6.2 Center-Manifold Reduction; 4.6.3 Projection Method; 4.7 Exercises; 5 Forced Oscillations of the Duffing Oscillator; 5.1 Primary Resonance; 5.2 Subharmonic Resonance of Order One-Third 327 $a5.3 Superharmonic Resonance of Order Three5.4 An Alternate Approach; 5.4.1 Subharmonic Case; 5.4.2 Superharmonic Case; 5.5 Exercises; 6 Forced Oscillations of SDOF Systems; 6.1 Introduction; 6.2 Primary Resonance; 6.3 Subharmonic Resonance of Order One-Half; 6.4 Superharmonic Resonance of Order Two; 6.5 Subharmonic Resonance of Order One-Third; 7 Parametrically Excited Systems; 7.1 The Mathieu Equation; 7.1.1 Fundamental Parametric Resonance; 7.1.2 Principal Parametric Resonance; 7.2 Multiple-Degree-of-Freedom Systems; 7.2.1 The Case of Near 2+1; 7.2.2 The Case of Near 2-1 327 $a7.2.3 The Case of Near 2+1 and 3-2 330 $aBased on a successful text, this second edition presents different concepts from dynamical systems theory and nonlinear dynamics. The introductory text systematically introduces models and techniques and states the relevant ranges of validity and applicability. New to this edition:3 new chapters dedicated to Maps, Bifurcations of Continuous Systems, and Retarded Systems Key features:Retarded Systems has become a topic of major importance in several applications, in mechanics and other areasProvides a clear operational framework for conscious use of co 606 $aNormal forms (Mathematics) 606 $aDifferential equations$xNumerical solutions 608 $aElectronic books. 615 0$aNormal forms (Mathematics) 615 0$aDifferential equations$xNumerical solutions. 676 $a512.9/44 676 $a512.944 700 $aNayfeh$b Ali Hasan$f1933-$021715 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910130959903321 996 $aThe method of normal forms$91920467 997 $aUNINA