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Discontinuous Contour

  • To: mathgroup at smc.vnet.net
  • Subject: [mg132120] Discontinuous Contour
  • From: Narasimham <mathma18 at gmail.com>
  • Date: Sat, 14 Dec 2013 04:03:39 -0500 (EST)
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pend = {PH''[t] + 10 Cos[PH[t]] (4 - 1 Cos[TH[t]])/20. == 0, 
  PH[0] == .5, PH'[0] == .4, TH''[t] + 2. Sin[TH[t]] == 0, 
  TH[0] == 1.1, TH'[0] == .8}; NDSolve[pend, {PH, TH}, {t, 0, 40}];
{ph[t_], th[t_]} = {PH[t], TH[t]} /. First[%];
a = 0.25; b = 4.; XYZ = {b Sin[ph[t]], (a + b Cos[ph[t]]) Sin[
    th[t]], -(a + b Cos[ph[t]]) Cos[th[t]]};
Projn1 = ParametricPlot3D[{b Sin[ph[t]], (a + b Cos[ph[t]]) Sin[
     th[t]], -5}, {t, 0, 40}, PlotStyle -> {Red, Thick}]
Projn2 = ParametricPlot3D[{b Sin[ph[t]], (a + b Cos[ph[t]]) Sin[
     th[t]], -5 (t 10^-7 + 1)}, {t, 0, 40}, PlotStyle -> {Red, Thick}]

Line Plots in projection do not compute as a continuous variable but maybe only as ListPlot at given parameter points. Low interval contour smoothness is required just like for surfaces automatically for continuous 2D Contours also. An improvement seen by inclusion of a small Z coordinate, but is there a better way to it?

Regards
Narasimham



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