Nonlinear Differential Equations and Nonlinear Mechanics provides information pertinent to nonlinear differential equations, nonlinear mechanics, control theory, and other related topics. This book discusses the properties of solutions of equations in standard form in the infinite time interval.
Organized into 49 chapters, this book starts with an overview of the characteristic types of differential equation systems with small parameters. This text then explains the structurally stable fields on a differentiable two manifold are the ones that exhibit the simplest features. Other chapters explore the canonic system of hyperbolic partial differential equations with fixed characteristics. This book discusses as well the monofrequent oscillations that are predominantly near one or the other of the linear modes of motion. The final chapter deals with the existence and asymptotic character of solutions of the nonlinear boundary value problem.
This book is a valuable resource for pure and applied mathematicians. Aircraft engineers will also find this book useful.
List of Contributors Preface The Method of Integral Manifolds in the Theory of Nonlinear Oscillations Sur un Théorème de Seifert sur les Trajectoires Fermées de Certains Champs de Vecteurs Generic Properties of Differential Equations The Density Theorem for Structurally Stable Systems on a Two Dimensional Manifold Beurteilung Nichtlinearer Systeme auf der Grundlage der Strukturstabilität Periodic Solutions of Hyperbolic Partial Differential Equations Coupling in Certain Classes of Weakly Nonlinear Vibrating Systems Perturbation Theory for Almost Periodic Solutions for Undamped Nonlinear Differential Equations Asymptotic System of a Perturbed System On some New Long Periodic Solutions of the Plane Restricted Three Body Problem Continuous Groups and Autosynartetic Solutions Autosynartetic Families of Solutions Periodic Functions Generated as Solutions of Nonlinear Differential-Difference Equations Uniformly Valid Asymptotic Approximations for Certain Non-Linear Differential Equations New Directions of Research in the Theory of Differential Equations Some Aspects of Quasilinearization On the Differential Equations of Electrical Circuits and the Global Nature of the Solutions Differential-Difference Equations Transport Theory, Invariant Imbedding, and Two-Point Boundary Value Problems Numerical Study of Periodic Solutions of the van der Pol Equation Finite Elastic Deformation of a Plane Strain Wedgeshaped Radial Crack in a Compressible Cylinder Wave Propagation in Non-Simple Media Some Nonlinear Systems of Differential Equations Equivalent to Linear Systems A Class of Characteristic-Value Problems Association of Partial Differential Equations with Ordinary Ones and Its Applications Stochastic Approximation and Its Application to Problems of Prediction and Control Synthesis Boundedness and Stability Discrete Time Optimal Control Systems The Principle of Optimal Evolution A Geometric Interpretation of Pontryagin's Maximum Principle On the A
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- © Academic Press 1963
- 1st January 1963
- Academic Press
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