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Mathematica

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    $\begingroup$ The problem is with plotting, not NDSolve. Try setting the options PlotPoints -> 100, MaxRecursion -> 8 on ParametricPlot. $\endgroup$ Commented Nov 18, 2013 at 14:04
  • $\begingroup$ Right, this solves it. Any idea why it doesn't plot smooth functions by default? $\endgroup$ Commented Nov 18, 2013 at 14:06
  • $\begingroup$ Because MaxRecursion limits how much effort the plotting function may put into making it smooth. Some functions would take a very long time to make smooth. $\endgroup$ Commented Nov 18, 2013 at 14:34
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    $\begingroup$ The number of points that will be plotted is limited for performance reasons, as in all other systems. Mathematica actually has an advantage here because it does adaptive plotting. First it divides the {t,0,20} interval into PlotPoints number of equal parts and computes the function at each point. Many other systems will do only this much, and will typically give you some jaggedness. But Mathematica will look at each segment pair and if their angle is large enough (i.e. if they look jagged), it will subdivide them to make the plot smoother. Then it repeats this up to MaxRecursion times. $\endgroup$ Commented Nov 18, 2013 at 18:26