quartic egg curve


last updated: 20040509 
The curve is formed by a
set of two attached sticks, as follows:
A stick OP is fixed in O, and attached to a second stick in
point P. The second stick AQ is free to move (in point A) along the xaxis.
Then the path of Q forms the quartic egg curve.
An Italian
animation shows the construction very clearly.
The equation above follows from the expressions for the x and ycoordinate of the
point Q ^{1)}.
notes
1) As follows (let c=1):
x_{Q} = b cos a_{1}  cos a_{2}
y_{Q} = b sin a_{1} + sin a_{2}
with
sin a_{2} = a sin a_{1}
Remark: the parameters a and b have been transposed.
