Advertisement

Stability of a Mechanical Equilibrium

  • N. Rouche
  • P. Habets
  • M. Laloy
Part of the Applied Mathematical Sciences book series (AMS, volume 22)

Abstract

This chapter is devoted to stability questions concerning mechanical equilibria, or in other words to stability of critical points for differential equations having the Lagrangian or Hamiltonian form, with or without friction forces. The central theorem in this context was stated by J.L. Lagrange [1788]: roughly speaking, it asserts that a mechanical equilibrium of a conservative system is stable at each point where the potential function is strictly minimum. Lagrange himself (as well as S.D. Poisson [1838]) failed to give a proof for a potential function more general than a quadratic form. G. Lejeune-Dirichlet [1846] gave an elegant general proof which yielded the model for the entire direct method of Liapunov.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag, New York Inc. 1977

Authors and Affiliations

  • N. Rouche
    • 1
  • P. Habets
    • 1
  • M. Laloy
    • 1
  1. 1.Institut de Mathématique Pure et AppliquéeU.C.L.Louvain-la-NeuveBelgium

Personalised recommendations