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Elimination of parameter

  1. Mar 16, 2009 #1
    basically i need to convert the following parametric equation:
    x=a cos (T) + b cos (T/2)
    y=a sin (T) + b sin (T/2); where a and b are coefficients

    to cartesian form: y = f(x)

    i need it in that form so i can do calculus analysis for an improved engine design i hope to develop. thanks in advance for any help.

    ps. if it helps any its a graph of an epitrochoid.
    so ive read that it may be impossible to solve but free brownie points to those that can!
     
    Last edited: Mar 16, 2009
  2. jcsd
  3. Mar 16, 2009 #2
    Write the trigonometric functions as exponential functions using euler's identity. Replace exp(iT/2) with z. Multiply though by z^2. Solve the fourth order polynomial symbolically (Yicks!) for z. T=2*angle(z). This will give you Z in terms of x and then you can then substitute this result into the seconded equation to get y in terms of x.

    It's going to be extremely messing because the symbolic solution of a forth order polynomial is not simple. I'd give it a try if you pay me or find me a job. Best of luck :)

    P.S. That's a cool looking shape.
    http://en.wikipedia.org/wiki/Epitrochoid
     
    Last edited: Mar 16, 2009
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