LEADER 04033nam 2200661Ia 450 001 9910784729503321 005 20230721030934.0 010 $a1-281-91872-5 010 $a9786611918729 010 $a981-270-910-X 035 $a(CKB)1000000000405444 035 $a(EBL)1679751 035 $a(OCoLC)879023979 035 $a(SSID)ssj0000247132 035 $a(PQKBManifestationID)11227066 035 $a(PQKBTitleCode)TC0000247132 035 $a(PQKBWorkID)10195103 035 $a(PQKB)10770572 035 $a(MiAaPQ)EBC1679751 035 $a(WSP)00006542 035 $a(Au-PeEL)EBL1679751 035 $a(CaPaEBR)ebr10255401 035 $a(CaONFJC)MIL191872 035 $a(EXLCZ)991000000000405444 100 $a20080324d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSmooth and nonsmooth high dimensional chaos and the melnikov-type methods$b[electronic resource] /$fJan Awrejcewicz, Mariusz M. Holicke 210 $aNew Jersey $cWorld Scientific$dc2007 215 $a1 online resource (318 p.) 225 1 $aWorld Scientific series on nonlinear science. Series A ;$vv. 60 300 $aDescription based upon print version of record. 311 $a981-270-909-6 320 $aIncludes bibliographical references (p. 285-289) and index. 327 $aContents; Preface; 1. A Role of the Melnikov-Type Methods in Applied Sciences; 1.1 Introduction; 1.2 Application of the Melnikov-type methods; 2. Classical Melnikov Approach; 2.1 Introduction; 2.2 Geometric interpretation; 2.3 Melnikov's function; 3. Homoclinic Chaos Criterion in a Rotated Froude Pendulum with Dry Friction; 3.1 Mathematical Model; 3.2 Homoclinic Chaos Criterion; 3.3 Numerical Simulations; 4. Smooth and Nonsmooth Dynamics of a Quasi- Autonomous Oscillator with Coulomb and Viscous Frictions; 4.1 Stick-Slip Oscillator with Periodic Excitation 327 $a4.2 Analysis of the Wandering Trajectories4.3 Comparison of Analytical and Numerical Results; 5. Application of the Melnikov-Gruendler Method to Mechanical Systems; 5.1 Mechanical Systems with Finite Number of Degrees-of- Freedom; 5.2 2-DOFs Mechanical Systems; 5.3 Reduction of the Melnikov-Gruendler Method for 1-DOF Systems; 6. A Self-Excited Spherical Pendulum; 6.1 Analytical Prediction of Chaos; 6.2 Numerical Results; 7. A Double Self-excited Duffing-type Oscillator; 7.1 Analytical Prediction of Chaos; 7.2 Numerical Simulations; 7.3 Additional Numerical Example 327 $a8. A Triple Self-Excited Du ng-type Oscillator8.1 Physical and Mathematical Models; 8.2 Analytical Prediction of Homoclinic Intersections; Bibliography; Index 330 $a This book focuses on the development of Melnikov-type methods applied to high dimensional dynamical systems governed by ordinary differential equations. Although the classical Melnikov's technique has found various applications in predicting homoclinic intersections, it is devoted only to the analysis of three-dimensional systems (in the case of mechanics, they represent one-degree-of-freedom nonautonomous systems). This book extends the classical Melnikov's approach to the study of high dimensional dynamical systems, and uses simple models of dry friction to analytically predict the occurren 410 0$aWorld Scientific series on nonlinear science.$nSeries A,$pMonographs and treatises ;$vv. 60. 606 $aChaotic behavior in systems 606 $aDifferentiable dynamical systems 606 $aNonlinear oscillators 615 0$aChaotic behavior in systems. 615 0$aDifferentiable dynamical systems. 615 0$aNonlinear oscillators. 676 $a003/.857 700 $aAwrejcewicz$b J$g(Jan)$059397 701 $aHolicke$b Mariusz M$01557409 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910784729503321 996 $aSmooth and nonsmooth high dimensional chaos and the melnikov-type methods$93820898 997 $aUNINA