Parametric Equations
HW: 11.1; 3,22
Why do we need parametric
equations?
• Consider the flight of a golf
ball…the motion consists of two
independent parts (Galileo’s
“big” insight):
• Falling motion or Galileo’s Law of
falling bodies in the vertical (y)
direction
• Uniform translational motion in the
horizontal (x) direction
“In Math”…
• Vertical motion:
• Horizontal
motion:
1 2
y(t )  vy t  gt
2
“t” is the parameter
x(t )  vx t
What path does a golf
ball follow?
140
120
x(m),y(m)
100
80
60
40
y(t) = -4.905t2 + 20t
20
0
0.0
1.0
2.0
3.0
4.0
5.0
t(s)
But how are x and y related to
each other?
A famous historical
example … the Cycloid
• What path does a point on the
rim of a circle trace as the
circle rolls at a constant rate
without slipping?
So, why do we need
parametric equations?
• By finding the suitable
parameterization you can
sometimes express
relationships between variables
that would otherwise be very
difficult to do.
Next lecture…
• Applying ideas of calculus to
parametric equations
• Read 11.2
• HW: 3, 15