On Stability of Some Newton Systems

• Autores: Marcelo Farias Caetano, Manuel Valentim de Pera Garcia
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 18, Nº 3, 2019, págs. 1001-1011
• Idioma: inglés
• DOI: 10.1007/s12346-019-00324-w
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• Resumen

  • 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, 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.