PARAMETRIC EQUATION OF
Suppose we start with
a circle with center P. Let A be a point on the circumference.
At time t=0, let the point A be on the origin O (0,0). At time
t, the circle would have moved forward such that, the co-ordinates
of A are (x,y) and the co-ordinates of B are (m,n).
Now in time t, the point
A would have described a distance = R theta along the circumference.
This is also the horizontal distance moved by the center of the
This horizontal distance
moved by the center will be from Origin to the point Q = x + AB
This gives us or
Considering the Vertical
distance, Y = PQ-PB =
Thus we have
We also know that the
circle would be moving with a constant angular velocity, W. Where
theta = Wt.
Thus the equations can
be represented as
x = R Wt - R Sin (Wt)
y = R - R Cos(Wt)
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