This book makes more widely accessible the text of Lyapunov's major memoir of the general problem of the stability of motion. Translated by A. T. Fuller (University of Cambridge), the work is now available for the first time in the English language, and marked the centenary of the Russian publication in the late 1800s. Including a biography of Lyapunov and a comprehensive bibliography of his work, this excellent volume will prove to be of fundamental interest to all those concerned with the concept of the stability of motion, boundaries of stability, and with nonlinear dynamics.
Author(s): Aleksandr Mikhailovich Lyapunov
Edition: 1
Publisher: CRC Press
Year: 1992
Language: English
Commentary: Added correct bookmarks to previously uploaded version.
Pages: 270
Cover
Contents
Guest Editorial
The general problem of the stability of motion
Preface
Chapter I. Preliminary analysis
Generalities on the question under study
On certain systems of linear differential equations
On a general case of the differential equations of disturbed motion
Some general propositions
Chapter II. Study of steady motion
Linear differential equations with constant coefficients
Study of the differential equations of the disturbed motion
First case. Determinantal equations with one root equal to zero
Second case. Determinantal equation with two purely imaginary roots
Periodic solutions of the differential equations of disturbed motion
Chapter III. Study of periodic motion
Linear differential equations with periodic coefficients
Some propositions relating to the characteristic equation
Study of the differential equations of the disturbed motion
First case. Characteristic equation with one root equal to unity
Second case. Characteristic equation with two complex roots with moduli equal to unity
A generalization
NOTE. Complement to the general theorems on stability
Index
Biography of A. M. Lyapunov
Bibliography of A. M. Lyapunov's work
