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Inversion Problem for the Lagrange Theorem on the Stability of Equilibrium and Related Problems

  • Valery V. Kozlov
  • Stanislav D. Furta
Chapter
  • 1.2k Downloads
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

In this chapter we consider problems that we will solve by a method that we originally used for proving instability in cases where linearized equations alone were insufficient. This first section will serve mostly as an introduction. Here we will outline a range of problems and formulate a number of theorems on stability for which converse assertions are introduced in the final sections, their proof being based on the construction of asymptotic solutions. In these theorems the principal stability condition will be the presence of an isolated minimum of some function that plays the role of the potential energy of the system.

Keywords

Asymptotic Stability Equilibrium Position Asymptotic Solution Invariant Manifold Center Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Valery V. Kozlov
    • 1
  • Stanislav D. Furta
    • 2
  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia
  2. 2.Faculty for Innovative and Technological BusinessRussian Academy of National Economy and Public AdministrationMoscowRussia

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