Differential Equations

Stan Wagon ()
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Stan Wagon: Macalester College, Department of Mathematics and Computer Science

Chapter 14 in Mathematica in Action, 2010, pp 363-397 from Springer

Abstract: Abstract A damped pendulum can be described by the differential equation x″ = −x ′−10sinx, where x represents the angular displacement and −x′ is the damping term. The image shows 24 solutions in the phase plane; the solutions almost always converge to one of the equilibrium points, the exception being the separatrix curves. The image also shows the equilibrium points in yellow, the nullcline curves (where x or x ′ vanish) in black, and the regions defined by the nullcline curves (where the direction of motion is either northeast, southeast, northwest, or southwest) in pastel colors. All of these features can be computed for any autonomous two-dimensional system.

Keywords: Equilibrium Point; Phase Plane; Duffing Equation; Wheel Center; Symbolic Solution (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-387-75477-2_15

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DOI: 10.1007/978-0-387-75477-2_15

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