Non-Linear Spring Equations and Stability

Autor/inn/en	Fay, Temple H.; Joubert, Stephan V.
Titel	Non-Linear Spring Equations and Stability
Quelle	In: International Journal of Mathematical Education in Science and Technology, 40 (2009) 8, S.1069-1084 (16 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
Schlagwörter	Equations (Mathematics); Mathematics Instruction; Mathematical Models; Mathematical Concepts; Problem Solving; Validity; Mathematical Logic; Topology + Suchen Sie Ihr Suchwort? Equations; Mathematics; Gleichungslehre; Mathematics lessons; Mathematikunterricht; Mathematical model; Mathematisches Modell; Problemlösen; Gültigkeit; Mathematical logics; Mathematische Logik; Topologie
Abstract	We discuss the boundary in the Poincare phase plane for boundedness of solutions to spring model equations of the form [second derivative of]x + x + epsilonx[superscript 2] = Fcoswt and the [second derivative of]x + x + epsilonx[superscript 3] = Fcoswt 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. (Contains 17 figures.) (As Provided).
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Update	2017/4/10