Publisher:

Chapman & Hall/CRC

Number of Pages:

255

Price:

89.95

ISBN:

0415310083

Date Received:

Wednesday, December 1, 2004

Reviewable:

No

Reviewer Email Address:

Series:

Stability and Control: Theory, Methods, and Applications 21

Publication Date:

2004

Format:

Hardcover

Audience:

Category:

Monograph

PRELIMINARIES

Introduction

Main Symbols

Asymptotic Series and their Properties

Poincarâ€š's Theorem on Asymptotic Approximations of Solutions of Differential Equations

Geometric Interpretation of Solutions of Oscillating Systems

On the Method of Characteristics for Quasi-linear First-Order Partial Differential Equations: Method of Characteristics

Iterative Variant of the Poincarâ€š-Lyapunov Small Parameter Method

Comments and References

AVERAGING PRINCIPLE FOR MULTI-FREQUENCY SYSTEMS OF DIFFERENTIAL EQUATIONS

Introduction

Mathematical Averaging Principle

Classification of Systems of Differential Equations where Resonances are Possible

The Basis of the Asymptotic Theory for Locally Nonresonance Systems

Initial Conditions for Comparison Equations

Averaging Operator for Time-Independent Disturbances

Asymptotic Theory of Systems with their Paths Passing through Resonance Points

The Algorithm of Joining of Resonance and Nonresonance Path Sections

Periodic and Quasi-Periodic Oscillations in the Van der Pol Oscillator System

Study of Multi-frequency Systems with their Solutions Not Remaining Close to Resonance Points

Study of Multi-frequency Systems Belonging to Class II

Multi-frequency Systems with their Solutions Not Leaving the Neighborhood of a Resonance Point

Comments and References

SOME RESONANCE PROBLEMS OF NONLINEAR MECHANICS

Newtonian Three-Body Problem

The Problem of Justification of the Averaging Principle in the Bounded Newtonian Three-Body Problem

Construction of Explicit Solutions of Averaged Differential Equations of the Bounded Three-Body Problem in the Case of Resonance

Quasi-Periodic Solutions of Resonance Hamiltonian Systems

Motion of a Geostationary Satellite

Averaging Method in the Theory of Partial Differential Equations

Energy Method of Construction of Amplitude-Phase Equations

Averaging Method and Maximum Principle in Boundary Value Problems

Comments and References

NUMERICAL-ANALYTIC METHODS

Construction of Lyapunov Transform for a Linear System with Periodic Coefficients

Construction of Green and Lyapunov Matrices

Direct Numerical-Analytic Method of Construction of Periodic Solutions

Construction of Periodic Solutions in Hill's Problem of Lunar Motion

Numerical-Analytic Construction of Mathieu Functions

Algorithm for Construction of Solutions of the Plane Bounded Three-Body Problem

Numerical-Analytic Implementation of Krylov-Bogolyubov Transform

Comments and References.

Introduction

Main Symbols

Asymptotic Series and their Properties

Poincarâ€š's Theorem on Asymptotic Approximations of Solutions of Differential Equations

Geometric Interpretation of Solutions of Oscillating Systems

On the Method of Characteristics for Quasi-linear First-Order Partial Differential Equations: Method of Characteristics

Iterative Variant of the Poincarâ€š-Lyapunov Small Parameter Method

Comments and References

AVERAGING PRINCIPLE FOR MULTI-FREQUENCY SYSTEMS OF DIFFERENTIAL EQUATIONS

Introduction

Mathematical Averaging Principle

Classification of Systems of Differential Equations where Resonances are Possible

The Basis of the Asymptotic Theory for Locally Nonresonance Systems

Initial Conditions for Comparison Equations

Averaging Operator for Time-Independent Disturbances

Asymptotic Theory of Systems with their Paths Passing through Resonance Points

The Algorithm of Joining of Resonance and Nonresonance Path Sections

Periodic and Quasi-Periodic Oscillations in the Van der Pol Oscillator System

Study of Multi-frequency Systems with their Solutions Not Remaining Close to Resonance Points

Study of Multi-frequency Systems Belonging to Class II

Multi-frequency Systems with their Solutions Not Leaving the Neighborhood of a Resonance Point

Comments and References

SOME RESONANCE PROBLEMS OF NONLINEAR MECHANICS

Newtonian Three-Body Problem

The Problem of Justification of the Averaging Principle in the Bounded Newtonian Three-Body Problem

Construction of Explicit Solutions of Averaged Differential Equations of the Bounded Three-Body Problem in the Case of Resonance

Quasi-Periodic Solutions of Resonance Hamiltonian Systems

Motion of a Geostationary Satellite

Averaging Method in the Theory of Partial Differential Equations

Energy Method of Construction of Amplitude-Phase Equations

Averaging Method and Maximum Principle in Boundary Value Problems

Comments and References

NUMERICAL-ANALYTIC METHODS

Construction of Lyapunov Transform for a Linear System with Periodic Coefficients

Construction of Green and Lyapunov Matrices

Direct Numerical-Analytic Method of Construction of Periodic Solutions

Construction of Periodic Solutions in Hill's Problem of Lunar Motion

Numerical-Analytic Construction of Mathieu Functions

Algorithm for Construction of Solutions of the Plane Bounded Three-Body Problem

Numerical-Analytic Implementation of Krylov-Bogolyubov Transform

Comments and References.

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