04066nam 2200673Ia 450 991045121380332120200520144314.01-281-91872-59786611918729981-270-910-X(CKB)1000000000405444(EBL)1679751(OCoLC)879023979(SSID)ssj0000247132(PQKBManifestationID)11227066(PQKBTitleCode)TC0000247132(PQKBWorkID)10195103(PQKB)10770572(MiAaPQ)EBC1679751(WSP)00006542(Au-PeEL)EBL1679751(CaPaEBR)ebr10255401(CaONFJC)MIL191872(EXLCZ)99100000000040544420080324d2007 uy 0engur|n|---|||||txtccrSmooth and nonsmooth high dimensional chaos and the melnikov-type methods[electronic resource] /Jan Awrejcewicz, Mariusz M. HolickeNew Jersey World Scientificc20071 online resource (318 p.)World Scientific series on nonlinear science. Series A ;v. 60Description based upon print version of record.981-270-909-6 Includes bibliographical references (p. 285-289) and index.Contents; 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 Excitation4.2 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 Example8. A Triple Self-Excited Du ng-type Oscillator8.1 Physical and Mathematical Models; 8.2 Analytical Prediction of Homoclinic Intersections; Bibliography; Index 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 occurrenWorld Scientific series on nonlinear science.Series A,Monographs and treatises ;v. 60.Chaotic behavior in systemsDifferentiable dynamical systemsNonlinear oscillatorsElectronic books.Chaotic behavior in systems.Differentiable dynamical systems.Nonlinear oscillators.003/.857Awrejcewicz J(Jan)59397Holicke Mariusz M888735MiAaPQMiAaPQMiAaPQBOOK9910451213803321Smooth and nonsmooth high dimensional chaos and the melnikov-type methods1985263UNINA