Anybody know the parametric form of an equation for a Cassini oval?
Thank you all for your help, but I don't know how to derive an equation of the form x(t) = |insert function of t|, y(t) = |insert function of t| from an equation in terms of x and y. Sorry, my friends; I'm going to have to ask for the explicit equations.
Cassini Oval: Parametric Equation
$\displaystyle x(\text{t})\text{=}\sqrt{\frac{m}{2}} \cos (t)$
$\displaystyle y(\text{t})\text{=}\sqrt{\frac{m}{2}} \sin (t)$
$\displaystyle m\text{=}2 \sqrt{\left(b^4-a^4\right)+a^4 \cos ^2(2 t)}+2 a^2 \cos (2 t)$
$\displaystyle 0<t\leq 2\pi$ and a<b
If a>b, this parametric equation generates only parts of Cassini Oval.
Cartesian to polar to parametric form ...
http://online.redwoods.cc.ca.us/inst...en/CalcPpr.pdf