International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics

International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics

1st Edition - January 1, 1963

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  • Editor: Joseph Lasalle
  • eBook ISBN: 9780323147309

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Description

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.

Table of Contents


  • 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 Accessibility Problem in Control Theory

    Time Optimal Control of Linear Systems with Bounded Controls

    Controllable Stability and Equivalent Nonlinear Programming Problem

    Periodic Solutions of Singular Perturbation Problems

    Ultimately Periodic Behavior in a Class of Non-linear Servomechanisms

    Determining the Switching Criterion for Time-Optimal Control

    On the Pontryagin Maximum Principle

    The Nonlinear Effect, Arising from White Noise and the Flicker Effect, in Nuclear Resonance Spectrometers of the "Marginal Oscillator" Type

    L'Extension de la Méthode de Nyquist aux Boucles Non-Linéaires. Application à L'Éitude de la Stabilité des Réacteurs Nucléaires

    A Contribution to Liapunov's Second Method: Nonlinear Autonomous Systems

    An Analysis of the Bistability of the Parametron

    Liapunov Functions and Comparison Theorems

    Structures Transverse to a Vector Field

    Systems of Differential Equations without Linear Terms

    Prolongations and Generalized Liapunov Functions

    Stability under Perturbations in Generalized Dynamical Systems

    A Functional-Differential System of Neutral Type Arising in a Two-Body Problem of Classical Electrodynamics

    Asymptotic Solutions of a Linear Ordinary Differential Equation of nth Order about a Simple Turning Point

    A Boundary Value Problem for a Singularly Perturbed System of Nonlinear Differential Equations

    Author Index

    Subject Index

Product details

  • No. of pages: 520
  • Language: English
  • Copyright: © Academic Press 1963
  • Published: January 1, 1963
  • Imprint: Academic Press
  • eBook ISBN: 9780323147309

About the Editor

Joseph Lasalle

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