Non-linear spring equations and stability

• Autores: Temple H. Fay, S.V. Joubert
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 40, Nº. 8, 2009, págs. 1069-1084
• Idioma: inglés
• DOI: 10.1080/00207390902759576
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• Resumen

  • We discuss the boundary in the Poincare phase plane for boundedness of solutions to spring model equations of the form [image omitted] and [image omitted]and report the results of a systematic numerical investigation on the global stability of solutions to initial value problems as the initial conditions are allowed to vary. We demonstrate that the unforced spring models explain some of the unbounded behaviour observed with the forced models and thus give at least an idea of where to expect bounded behaviour to occur. We also discuss the behaviour when viscous damping is added to the unforced models.