       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