General Problem of the Stability Of Motion
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.
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Study of the convergence of these series in the case where the arbitrary
On certain systems of linear differential equations
l0 Reducible systems of equations
Ensuing consequences relevant to stability
l6 Fundamental propositions
Study of steady motion
Biography of A M Lyapunov
Bibliography of A M Lyapunovs work
able absolute value absolutely convergent arbitrary constants assumption become zero bounded functions characteristic equation characteristic number coefficients psa conclude consequence constant coefficients constant g cosines of integer deduce defined determinant determinantal equation disturbed ensemble of terms equal equation of system equations l5 equilibrium expansions expression finite functions Xs holomorphic functions homogeneous functions hypothesis identically zero independent solutions indicated inequalities integer multiples Kharkov let us consider Let us suppose limit linear differential equations linear forms moreover motion is unstable multiple roots negative non-zero obtain partial differential equations periodic functions periodic solution periodic with respect positive integer powers positive number positive-definite function preceding problem proposition quadratic form real values reduce replace represent right-hand side Russian satisfying equations satisfying the conditions Section l6 series ordered sines and cosines substitution sufficiently small system 45 system of differential system of equations terms of degree theorem undisturbed motion variables