Mathematica 9 is now available
Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2010

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Plotting Quartic Solutions in Polar Coordinates

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112500] Re: Plotting Quartic Solutions in Polar Coordinates
  • From: "David Park" <djmpark at comcast.net>
  • Date: Fri, 17 Sep 2010 06:43:29 -0400 (EDT)

Ed,

I take it that you want to plot the curve and not the roots of the equation
(which I think could also be done as a function of the "a" parameter).

This is easily done with the Presentations package. We use a ContourPlot,
which plots in the r, phi plane, and then transform to Cartesian coordinates
using DrawingTransform. DrawingTransform contains pure functions for x and y
in terms of r (#1) and phi (#2).

<< Presentations` 

quartic[a_][r_, \[Phi]_] := r^4 - (2 Cos[2 \[Phi]]) r^2 - (a - 1) 

A specific case:

Draw2D[
 {ContourDraw[
    quartic[2][r, \[Phi]] == 0, {r, 0, 2}, {\[Phi], 0, 2 \[Pi]}] /. 
   DrawingTransform[#1 Cos[#2] &, #1 Sin[#2] &]},
 Frame -> True] 

Within a Manipulate statement:

Manipulate[
 Draw2D[
  {ContourDraw[
     quartic[a][r, \[Phi]] == 0, {r, 0, 2}, {\[Phi], 0, 2 \[Pi]},
     PerformanceGoal -> "Quality"] /. 
    DrawingTransform[#1 Cos[#2] &, #1 Sin[#2] &]},
  PlotRange -> 2,
  Frame -> True],
 {a, 0.1, 5, Appearance -> "Labeled"}] 


David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/  


From: Ed Frank [mailto:satchelp at earthlink.net] 


I have used "Solve" in (M7HE) to provide solutions to a Quartic equation in
(r,Phi), and have attempted to plot the results in Polar coordinates without
much success.
Can I send you what I have done - in an email attachment perhaps - and ask
for your comments?
The equation involves the 2 variables (r, Phi) and a single, constant
(though adjustable) parameter:
r^4 - (2 Cos[2*[Phi]]) r^2 - (a - 1) == 0
These are "Cassinian Ovals" for different vales of "a".

I think part of the problem may be in the self-defined formulas I created to
consolidate the solution(s).
PolarPlot seems to plot a Test constant value OK, but won't plot my solution
formulas.

Thanks,
Ed Frank
satchelp at earthlink.net





  • Prev by Date: Re: New Version 3 Presentations
  • Next by Date: Map Correlation[] across sublists of matrices
  • Previous by thread: Re: Plotting Quartic Solutions in Polar Coordinates
  • Next by thread: ImagePadding and PlotRange anomaly