Textbook in PDF format

This may be considered as a second (but greatly enlarged) edition of the author’s well-known Introduction to nonlinear mechanics. The field it covers is so vast and complex and has attracted so much attention that, lengthy as the volume is, it contains no more than very brief, but masterly, accounts of many of the topics. The author is not greatly concerned to develop abstract mathematical theories but refers repeatedly to applications and to experiment.
He gives ample references to the literature, especially to the work of the Russians, whose contribution to this theory is of course, outstanding. To anyone interested in nonlinear problems the book will be obviously essential; the author’s name is sufficient guarantee of that.
The list of contents gives some idea of the book’s wide scope:
Part I: Qualitative Methods: Phase Plane—Singular Points; Nonlinear Conservative Systems; Limit Cycles of Poincaré; Geometrical Analysis of Periodic Solutions; Stability (Variational Equations: Characteristic Exponents); Stability (Second Method of Liapounov); Theory of Bifurcations; Cylindrical and Toroidal Phase Spaces.
Part II: Quantitative Methods: Introduction; Perturbation Method; Periodic Solutions (Poincaré); Oscillations in Systems with Several Degrees of Freedom, Almost Periodic Oscillations in Nearly Linear Systems; Determination of Characteristic Exponents; Asymptotic Methods; Asymptotic Methods of Krylov—Bogoliubov—Mitropolsky (Nonautonomous Systems, Nonstationary Phenomena); Strosboscopic Method; Generalization of Nyquist’s Diagram for Nonlinear Systems.
Part III: Oscillations of Nearly Linear Systems: Introduction; Synchronization; Nonlinear Resonance; Parametric Excitation; Oscillations caused by Retarded Actions; Topology of Lienard’s Equation in a Parameter Space; Interaction of Nonlinear Oscillation; Asynchronous Action; Systems with Inertial Nonlinearities.
Part IV: Relaxation Oscillations: Introduction; Discontinuous Theory of Relaxation Oscillation; Application of the Discontinuous Theory to Electrical Problems; Application of the Discontinuous Theory to Mechanical Problems; Discontinuous Theory of Vogel; Asymptotic Methods; Piecewise Linear Idealization