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0
2
π
1
2
Figure 1:
PlotCycloidArc(8.5)
Math98 HW4
The
cylcoid
is the plane curve traced out by a point on a circle as the circle rolls without slipping on a
straight line.
1
In this exercise we will use MATLAB to create an animation of a circle rolling on a straight
line, while a point on the circle traces the cycloid.
a.
Implement a MATLAB function of the form
function PlotCycloidArc(ArcLength)
.
This function takes in a positive number
ArcLength
and displays a snapshot of the cirle rolling (without
slipping) on the
x
axis while a point on the cirlce traces the cycloid. The circle is initially centered at
(0,1) and has radius 1, and the initial tracing point is taken to be (0
,
0). An example output is shown in the
above ±gure. As in the ±gure, plot the cycloid arc black, the circle blue, and use a red dot for the tracing point.
Hint
: If the circle has rolled for a length of arc
t
≥
0, the coordinates of the tracing point are (
t

sin
t,
1

cos
t
)
.
b.
Implement a MATLAB function of the form
function CycloidMovie(NumHumps,NumIntervals)
.
This function will output an animation of the circle rolling along a line while a point on the circle traces the
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This note was uploaded on 01/21/2012 for the course MATH 98 taught by Professor Instuctor during the Spring '08 term at University of California, Berkeley.
 Spring '08
 Instuctor
 matlab

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