# Partial Stability and Control

• V. I. Vorotnikov
Textbook

1. Front Matter
Pages i-xii
2. V. I. Vorotnikov
Pages 51-118
3. V. I. Vorotnikov
Pages 167-202
4. V. I. Vorotnikov
Pages 203-288
5. V. I. Vorotnikov
Pages 289-346
6. V. I. Vorotnikov
Pages 347-378
7. V. I. Vorotnikov
Pages 379-398
8. Back Matter
Pages 399-430

### Introduction

Unlike the conventional research for the general theory of stability, this mono­ graph deals with problems on stability and stabilization of dynamic systems with respect not to all but just to a given part of the variables characterizing these systems. Such problems are often referred to as the problems of partial stability (stabilization). They naturally arise in applications either from the requirement of proper performance of a system or in assessing system capa­ bility. In addition, a lot of actual (or desired) phenomena can be formulated in terms of these problems and be analyzed with these problems taken as the basis. The following multiaspect phenomena and problems can be indicated: • "Lotka-Volterra ecological principle of extinction;" • focusing and acceleration of particles in electromagnetic fields; • "drift" of the gyroscope axis; • stabilization of a spacecraft by specially arranged relative motion of rotors connected to it. Also very effective is the approach to the problem of stability (stabilization) with respect to all the variables based on preliminary analysis of partial sta­ bility (stabilization). A. M. Lyapunov, the founder of the modern theory of stability, was the first to formulate the problem of partial stability. Later, works by V. V. Rumyan­ tsev drew the attention of many mathematicians and mechanicians around the world to this problem, which resulted in its being intensively worked out. The method of Lyapunov functions became the key investigative method which turned out to be very effective in analyzing both theoretic and applied problems.

### Keywords

Control rotation solids stability system

#### Authors and affiliations

• V. I. Vorotnikov
• 1
1. 1.Nizhny Tagil CampusUral State Technical UniversityNizhny TagilRussia

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-4150-8
• Copyright Information Birkhäuser Boston 1998
• Publisher Name Birkhäuser Boston
• eBook Packages
• Print ISBN 978-1-4612-8675-2
• Online ISBN 978-1-4612-4150-8
• Buy this book on publisher's site
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