Synopses & Reviews
The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject.
"Hill's equation" connotes the class of homogeneous, linear, second order differential equations with real, periodic coefficients. This two part treatment encompasses the most pertinent, necessary information; only the theory's elementary facts are proved in full, with minimal use of sophisticated mathematics. Part I explains the basic theory: Floquet's theorem, characteristic values and intervals of stability, analytic properties of the discriminant, infinite determinants, asymptotic behavior of the characteristic values, theorems of Liapounoff and Borg, and related topics. Part II examines numerous details: elementary formulas, oscillatory solutions, intervals of stability and instability, discriminant, coexistence, and examples. Particular attention is given to stability problems and to the question of coexistence of periodic solutions.
Although intended for professional mathematicians and engineers, the volume is written so clearly and vigorously that it can be recommended for graduate students and advanced undergraduates. List of Symbols and Notations. List of Theorems, Lemmas, and Corollaries. References. Index.
Synopsis
This two-part treatment of Hill's equation encompasses the subject's most pertinent information, explaining both basic theory and numerous details, including elementary formulas, oscillatory solutions, intervals of stability and instability, discriminants, and coexistence. Particular attention is given to stability problems and the question of coexistence of periodic solutions. 1966 edition.
Synopsis
This concise treatment of Hill's equation--a theory with hundreds of applications in many areas of engineering and physics--presents the most pertinent and necessary facts with minimal use of sophisticated mathematics. Unabridged, corrected publication of the edition published by Interscience Publishers, New York, 1966.
Synopsis
This two-part treatment explains basic theory and details, including oscillatory solutions, intervals of stability and instability, discriminants, and coexistence. Particular attention to stability problems and coexistence of periodic solutions. 1966 edition.
Synopsis
This two-part treatment explains basic theory and details, including oscillatory solutions, intervals of stability and instability, discriminants, and coexistence. Particular attention to stability problems and coexistence of periodic solutions. 1966 edition.
Synopsis
This two-part treatment explains basic theory and details, including oscillatory solutions, intervals of stability and instability, discriminants, and coexistence. Particular attention to stability problems and coexistence of periodic solutions. 1966 edition.
Table of Contents
I. General Theory.
1. Basic Concepts.
2. Characteristic Values and Discriminant.
II. Details.
3. Elementary Formulas.
4. Oscillatory Solutions.
5. Intervals of Stability and Instability.
6. Discriminant.
7. Coexistence.
8. Examples.
List of Symbols and Notations.
List of Theorems, Lemmas, and Corollaries.
References.
Index.