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Qualitative Theory of Dynamical Systems

, Volume 18, Issue 3, pp 1001–1011 | Cite as

On Stability of Some Newton Systems

  • Marcelo Farias Caetano
  • Manuel Valentim de Pera GarciaEmail author
Article
  • 63 Downloads

Abstract

The aim of this paper is to study the stability of an equilibrium for the second order ordinary differential equation \(\ddot{q}=F(q), \; q \in \mathbb {R}^{2}\), which are the equations of motion of a point of mass under the action of force F. The smooth force F is not supposed to be gradient. We consider two situations separately, the case of systems which have an indefinite quadratic first integral and the situation where the forces point inwards to circumferences with center at the equilibrium point.

Keywords

Liapunov stability Non-conservative positional forces Central forces 

Notes

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Instituto de Matemática e EstatísticaUSP Departamento de Matemática AplicadaSão PauloBrazil
  2. 2.Instituto de Matemática e EstatísticaUSP Departamento de Matemática AplicadaSão PauloBrazil

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