## Advances in Stability Theory at the End of the 20th CenturyThis volume presents surveys and research papers on various aspects of modern stability theory, including discussions on modern applications of the theory, all contributed by experts in the field. The volume consists of four sections that explore the following directions in the development of stability theory: progress in stability theory by first approximation; contemporary developments in Lyapunov's idea of the direct method; the stability of solutions to periodic differential systems; and selected applications. Advances in Stability Theory at the End of the 20th Century will interest postgraduates and researchers in engineering fields as well as those in mathematics. |

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Advances in Stability Theory at the End of the 20th Century A.A. Martynyuk No preview available - 2002 |

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A.A. Martynyuk Advances in Stability analysis angular velocity assume axis bifurcation comparison system consider constant constructive m-exponent continuous function defined Diff differential systems dynamical systems eigenvalues Eqns equilibrium exists exponential stability exponents functional differential equations gyroscope implies impulsive inequality inertia integral investigation Izobov Lakshmikantham Lemma linear systems Lyapunov exponents Lyapunov function Lyapunov method Lyapunov problem Lyapunov stability Lyapunov stable Math Mathematical matrix mechanical system Mekh method Moscow Russian nonlinear systems obtained ordinary differential ordinary differential equations oscillations parameter parametric resonance periodic orbit periodic solutions perturbations positive definite Prikl problem of three proof real number rigid body rotation satisfied Section semiflow solution of equation solution x(t Stability of Motion Stability Theory steady-state motion string Suppose system 1a Theorem 3.1 three bodies tions uniformly asymptotically stable vector Lyapunov function vector norms vertical vibrations Volterra Xn(A zero solution

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Page viii - Introduction to the Series The problems of modern society are both complex and interdisciplinary. Despite the apparent diversity of problems, tools developed in one context are often adaptable to an entirely different situation. For example, consider the Lyapunov's well-known second method. This interesting and fruitful technique has gained increasing significance and has given a decisive impetus for modern development of the stability theory of differential equations. A manifest advantage of this...

Page ix - Martynyuk and AA Shestakov Volume 4 Control Theory and its Applications EO Roxin Volume 5 Advances in Nonlinear Dynamics edited by S. Sivasundaram and AA Martynyuk Volume 6 Solving Differential Problems by Multistep Initial and Boundary Value Methods L. Brugnano and D. Trigiante Volume 7 Dynamics of Machines with Variable Mass L.

Page ix - Boundary Value Methods, is a joint contribution by L. Brugnano (Italy) and D. Trigiante (Italy). Volume 7, Dynamics of Machines with Variable Mass, is by L. Cveticanin (Yugoslavia). Volume 8, Optimization of Linear Control Systems: Analytical Methods and Computational Algorithms, is a joint work by FA Aliev (Azerbaijan) and VB Larin (Ukraine). Volume 9, Dynamics and Control, is edited by G. Leitmann (USA), FE Udwadia (USA) and AV Kryazhimskii (Russia) and is a multiauthor volume. Volume 10, Volterra...

Page viii - ... to study the properties of this simpler dynamic system. It is also being realized that the same versatile tools can be adapted to discuss entirely different nonlinear systems, and that other tools, such as the variation of parameters and the method of upper and lower solutions provide equally effective methods to deal with problems of a similar nature. Moreover, interesting new ideas have been introduced which would seem to hold great potential. Control theory, on the other hand, is that branch...

Page ix - Due to the increased interdependency and cooperation among the mathematical sciences across the traditional boundaries, and the accomplishments thus far achieved in the areas of stability and control, there is every reason to believe that many breakthroughs await us, offering existing prospects for these versatile techniques to advance further. It is in this spirit that we see the importance of the 'Stability and Control...