International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics - 1st Edition - ISBN: 9780123956514, 9780323147309

International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics

1st Edition

Editors: Joseph Lasalle
eBook ISBN: 9780323147309
Imprint: Academic Press
Published Date: 1st January 1963
Page Count: 520
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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

Details

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

About the Editor

Joseph Lasalle