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Pb. 1.9 If the parametric equations of a curve are given by:

C: x = cos(t), y = sin(2t), and 0 < t < 2π

where the initial point is at x = 1, y = 0, and the final point is at x = 1, y = 0.
The curve so obtained is called a Lissajous figure. It has the shape of a fig-
ure 8 with two nodes in the x-direction and only one node in the y-direction.
What do you think the parametric equations should be if we wanted m
nodes on the x-axis and n nodes on the y-axis? Test your hypothesis by plot-
ting the results.

1.7.3 Plotting a 3-D Curve
Our next area of exploration is plotting 3-D curves.

Example 1.14
Plot the helix.

Solution: To plot a helical curve, we can imagine initially that a point is
revolving at a uniform speed around the perimeter of a circle. Now imagine
that as the circular motion is continuing, the point is moving away from the
x-y plane at some constant linear speed. The parametric representation of this
motion can be implemented in MATLAB through the following:

for m=1:201
th(m)=2*pi*.01*(m-1);
x(m)=cos(th(m));
y(m)=sin(th(m));
z(m)=th(m);
end
plot3(x,y,z)

In-Class Exercises
Pb. 1.10 In the helix of Example 1.14, what is the vertical distance (the pitch)
between two consecutive helical turns. How can you control this distance?
Find two methods of implementation.
Pb. 1.11 If instead of a circle in 2-D, as in the helix, the particle describes in
2-D a Lissajous pattern having two nodes in the y-direction and three nodes

© 2001 by CRC Press LLC