Regular and Chaotic Oscillations
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In this book the modern theory of both regular and chaotic nonlinear oscillations is set out, primarily, as applied to mechanical problems. The material is presented in a nontraditional manner with emphasis on the new results of the theory obtained partially by the author, who is one of the leading experts in the area. Among the up-to-date topics are synchronization and chaotization of self-oscillatory systems and the influence of weak random vibrations on the modification of characteristics and behavior of nonlinear systems. One of the purposes of the book is to enable readers to gain a thorough understanding of this theory and to show that it can be very useful in engineering investigations. The primary audience for this book is researchers working with different oscillatory processes and students interested in a thorough study of the general laws and applications of the theory of nonlinear oscillations.
1Introduction12The main analytical methods of studies of nonlinear oscillations in near-conservative systems93General properties of autonomous dynamical systems274Examples of natural oscillations in systems with one degree of freedom495Natural oscillations in systems with many degrees of freedom. Normal oscillations636Self-oscillatory systems with one degree of freedom897Self-oscillatory systems with one and a half degrees of freedom1078Examples of self-oscillatory systems with two or more degrees of freedom1379Synchronization and chaotization of self-oscillatory systems by an external harmonic force16110Interaction of two self-oscillatory systems. Synchronization and chaotization of self-oscillations20511Interaction of three or more self-oscillatory systems23712Oscillations of nonlinear systems excited by external periodic forces25513Parametric excitation of oscillations28914Changes in the dynamical behavior of nonlinear systems induced by high-frequency vibration or by noise323ADerivation of the approximate equation for the one-dimensional probability density373References377Index393
