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Math Help - Cassini ovals parametric equation?

  1. #1
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    Question Cassini ovals parametric equation?

    Anybody know the parametric form of an equation for a Cassini oval?
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  2. #2
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    Re: Cassini ovals parametric equation?

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    Lightbulb Re: Cassini ovals parametric equation?

    Cassini Oval in simple form of complex variables z, q1, q2:

    |z-\text{q1}| |z-\text{q2}|=b^2

    Attached Thumbnails Attached Thumbnails Cassini ovals  parametric equation?-cassini-oval.png  
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    Re: Cassini ovals parametric equation?

    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.
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    Lightbulb Re: Cassini ovals parametric equation?

    Cassini Oval: Parametric Equation


    x(\text{t})\text{=}\sqrt{\frac{m}{2}} \cos (t)

    y(\text{t})\text{=}\sqrt{\frac{m}{2}} \sin (t)

    m\text{=}2 \sqrt{\left(b^4-a^4\right)+a^4 \cos ^2(2 t)}+2 a^2 \cos (2 t)

    0<t\leq 2\pi and a<b

    If a>b, this parametric equation generates only parts of Cassini Oval.
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  6. #6
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    Re: Cassini ovals parametric equation?

    Cartesian to polar to parametric form ...

    http://online.redwoods.cc.ca.us/inst...en/CalcPpr.pdf
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