#Header Begins--Do not remove##################################################
#
#	Maple code to plot trochoidal functions.
#
#	(c) Eugene Fiume, University of Toronto, 1995.
#
#	You are permitted to use this code for noncommercial, educational
#	purposes only.  This header must not be removed from this file.
#
#Header Ends--Do not remove####################################################

#
#	First, the x and y parametric functions.
#
x := proc(a,r,u)
	a*u - r*sin(u);
end:

y := proc(r,u)
	r*cos(u)
end:

#
#	Just plot the parametric functions x,y.
#
plotXY := proc(a,r)
	local u;
	plot( {x(a,r,u), y(r,u)}, u=0..4*Pi,
		title=`Parametric functions x and y` );
end:

#
#	Plot the resulting trochoid.
#
plotTrochoid := proc(a,r)
	local u;
	plot( [x(a,r,u), y(r,u), u=0..4*Pi],
		title=`Trochoid`);
end:


#
#	Plot everything together.
#
plotAll := proc(a,r)
	local u;
	plot( {[x(a,r,u), y(r,u), u=-Pi..6*Pi], x(a,r,u), y(r,u)}, u=0..4*Pi,
		title=`Both the trochoid and its parametric functions`);
end:

#
#	Examples:
#
#	plotAll(0.75, 3.0);		# gives Figure 1.7