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Asymptotic Methods in Resonance Analytical Dynamics

E.A. Grebenikov, Yu.A. Mitropolsky and Yu.A. Ryabov
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2004
Number of Pages: 
255
Format: 
Hardcover
Series: 
Stability and Control: Theory, Methods, and Applications 21
Price: 
89.95
ISBN: 
0415310083
Category: 
Monograph
We do not plan to review this book.
PRELIMINARIES
Introduction
Main Symbols
Asymptotic Series and their Properties
Poincar‚'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 Poincar‚-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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