Nonlinear autonomous oscillations : analytical theory / Minoru Urabe.

Format:

Book

Author/Creator:

Urabe, Minoru, 1912-1975, author.

Series:

Mathematics in science and engineering ; volume 34.

Mathematics in science and engineering : a series of monographs and textbooks ; volume 34

Language:

English

Subjects (All):

Oscillations.

Nonlinear theories.

Physical Description:

1 online resource (343 p.)

Place of Publication:

New York : Academic Press, 1967.

Language Note:

English

Summary:

Nonlinear autonomous oscillations; analytical theory

Contents:

Front Cover; Nonlinear Autonomous Oscillations; Copyright Page; Contents; Preface; Chapter 1. Analysis of Vectors and Matrices; 1.1 Norms of Vectors and Matrices; 1.2 Canonical Forms of Matrices; 1.3 Sequences and Series of Matrices; 1.4 Logarithms of Matrices; 1.5 Differentiation and Integration of Matrices; Chapter 2. Basic Theorems Concerning Ordinary Differential Equations; 2.1 Fundamental Existence Theorems; 2.2 Dependence of the Solution on Initial Conditions and Parameters; Chapter 3. Linear Differential Systems; 3.1 Linear Homogeneous Systems; 3.2 Linear Nonhomogeneous Systems

Chapter 4. Orbits of Autonomous Systems4.1 Introduction; 4.2 Critical Points of Autonomous Systems; 4.3 Periodic Solutions and Closed Orbits; 4.4 Continuity of Orbits; Chapter 5. Moving Orthonormal Systems along a Closed Orbit; 5.1 A Method to Construct a Moving Orthonormal System along a Closed Orbit; 5.2 Equations of Orbits with Respect to the Moving Orthogonal System; 5.3 Multipliers of Solutions of the Normal Variation Equation; Chapter 6. Stability; 6.1 Definition of Stability; 6.2 Fundamental Theorems Concerning Stability; 6.3 Orbital Stability; 6.4 Orbital Stability of Critical Points

6.5 Orbital Stability of Periodic SolutionsChapter 7. Perturbation of Autonomous Systems; 7.1 Fundamental Formulas; 7.2 Periodic Solutions of the Perturbed System; 7.3 Stability of the Periodic Solution of the Perturbed System; Chapter 8. Perturbation of Fully Oscillatory Systems; 8.1 Universal Periods; 8.2 Preliminary Theorem; 8.3 Perturbation of a Fully Oscillatory System; 8.4 An Example; Chapter 9. Perturbation of Partially Oscillatory Systems; 9.1 The Reduced Form of the Partially Oscillatory System; 9.2 Perturbation of a Partially Oscillatory System

9.3 Stability of the Periodic Solution of the Perturbed System9.4 An Example; Chapter 10. Analysis of Two-Dimensional Autonomous Systems; 10.1 Fundamental Formulas; 10.2 Stability of a Periodic Solution of the Unperturbed System; 10.3 Perturbation; 10.4 Perturbation of a Fully Oscillatory System; 10.5 Fundamental Formulas for Analytic Systems; 10.6 Stability of a Periodic Solution of the Analytic Unperturbed System; 10.7 Perturbation of Analytic Systems; 10.8 Multiplicities of Closed Orbits; 10.9 Perturbation of Analytic Fully Oscillatory Systems

Chapter 11. Numerical Computation of Periodic Solutions11.1 A Method to Compute a Periodic Solution; 11.2 The Two-Dimensional Case; 11.3 Periodic Solutions of the Autonomous van der Pol Equation; 11.4 Remarks; Chapter 12. Center of the Autonomous System; 12.1 First Reduction; 12.2 The Universal Period of the Orbit; 12.3 The Canonical Form of the Autonomous System in the Neighborhood of the Center; Chapter 13. Inverse Problems Connected with Periods of Oscillations Described by x + g(x) = 0; 13.1 Preliminaries; 13.2 Lemmas; 13.3 The Period Function Associated with the Maximum Velocity

13.4 The Period Functions Associated with the Amplitude and the Half- Amplitudes

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-282-76981-2

9786612769818

0-08-095541-X

OCLC:

700688101