On Stability of Some Newton Systems View Full Text


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Article Info

DATE

2019-03-20

AUTHORS

Marcelo Farias Caetano, Manuel Valentim de Pera Garcia

ABSTRACT

The aim of this paper is to study the stability of an equilibrium for the second order ordinary differential equation q¨=F(q),q∈R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ddot{q}=F(q), \; q \in \mathbb {R}^{2}$$\end{document}, 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. More... »

PAGES

1001-1011

References to SciGraph publications

  • 2015-05. Projective dynamics and first integrals in REGULAR AND CHAOTIC DYNAMICS
  • 1980-06. An inversion of the Lagrange-Dirichlet stability theorem in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
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    http://scigraph.springernature.com/pub.10.1007/s12346-019-00324-w

    DOI

    http://dx.doi.org/10.1007/s12346-019-00324-w

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