Re: Plotting Quartic Solutions in Polar Coordinates

*To*: mathgroup at smc.vnet.net*Subject*: [mg112481] Re: Plotting Quartic Solutions in Polar Coordinates*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Fri, 17 Sep 2010 06:40:00 -0400 (EDT)

Manipulate[ With[ {r = Sqrt[x^2 + y^2], phi = ArcTan[x, y], m = 2}, ContourPlot[ r^4 - 2 Cos[2*phi] r^2 - (a - 1) == 0, {x, -m, m}, {y, -m, m}]], {a, .1, 4., .1, Appearance -> "Labeled"}] Bob Hanlon ---- Ed Frank <satchelp at earthlink.net> wrote: ============= 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