HW4 - 2 1 2 0 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

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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.

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HW4 - 2 1 2 0 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

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