>	with(DEtools):

 

>	phug:= [ diff(theta(t),t) = ( v(t)^2 - cos(theta(t))) / v(t),         diff(v(t),t)     = -sin(theta(t)) - R*v(t)^2 ];

 

>

 

(1)

 

>	R:=0; DEplot(phug, [ theta(t), v(t) ], t=0..40,

 

>	[[theta(0)=0, v(0)=2.5], [theta(0)=0, v(0)=.8]],

 

>	theta=-Pi/2..3*Pi, v=0..3,

 

>	linecolor=[blue,red], stepsize=0.1); phase:=%:

 

>

 

>	DEplot(phug, [ theta(t), v(t) ], t=0..10,

 

>	[[theta(0)=0, v(0)=2.5], [theta(0)=0, v(0)=.8]],

 

>	theta=-Pi/2..3*Pi, v=0..3,       scene=[t,theta],

 

>	linecolor=[blue,red], stepsize=0.1); thetaplot:=%:

 

>

 

>	DEplot(phug, [ theta(t), v(t) ], t=0..10,

 

>	[[theta(0)=0, v(0)=2.5], [theta(0)=0, v(0)=.8]],

 

>	theta=-Pi/2..3*Pi, v=0..3,       scene=[t,v],

 

>	linecolor=[blue,red], stepsize=0.1); vplot:=%:

 

>

 

>

 

>	with(plots):

 

>	display( array ([ phase, thetaplot, vplot ]));

 

>	R:='R': xphug:= [ diff(theta(t),t) = ( v(t)^2 - cos(theta(t))) / v(t),         diff(v(t),t)     = -sin(theta(t)) - R*v(t)^2 ,         diff(x(t),t)     = v(t)*cos(theta(t)),         diff(y(t),t)     = v(t)*sin(theta(t))];

 

(2)

 

>	R:=0; display( array([      DEplot(xphug, [ theta(t), v(t), x(t), y(t) ], t=0..10,

 

>	[[theta(0)=0, v(0)=2.5, x(0)=0, y(0)=4 ],           [theta(0)=0, v(0)=.8,  x(0)=0, y(0)=1 ]],

 

>	theta=-Pi/2..3*Pi, v=0..3, x=-1..6, y=0..7,         scene=[theta,v],

 

>	linecolor=[blue,red], stepsize=0.1, title="v,theta phase"),

 

>	DEplot(xphug, [ theta(t), v(t), x(t), y(t) ], t=0..10,

 

>	[[theta(0)=0, v(0)=2.5, x(0)=0, y(0)=4 ],           [theta(0)=0, v(0)=.8,  x(0)=0, y(0)=1 ]],

 

>	theta=-Pi/2..3*Pi, v=0..3, x=-1..6, y=0..7,         scene=[x,y], title="path of glider",

 

>	linecolor=[blue,red], stepsize=0.1)       ]));

 

>

 

>

 

>	R:=0.1; display( array([      DEplot(xphug, [ theta(t), v(t), x(t), y(t) ], t=0..10,

 

>	[[theta(0)=0, v(0)=2.5, x(0)=0, y(0)=4 ],           [theta(0)=0, v(0)=.8,  x(0)=0, y(0)=1 ]],

 

>	theta=-Pi/2..3*Pi, v=0..3, x=-1..6, y=0..7,         scene=[theta,v],

 

>	linecolor=[blue,red], stepsize=0.1, title="v,theta phase"),

 

>	DEplot(xphug, [ theta(t), v(t), x(t), y(t) ], t=0..10,

 

>	[[theta(0)=0, v(0)=2.5, x(0)=0, y(0)=4 ],           [theta(0)=0, v(0)=.8,  x(0)=0, y(0)=1 ]],

 

>	theta=-Pi/2..3*Pi, v=0..3, x=-1..6, y=0..7,         scene=[x,y], title="path of glider",

 

>	linecolor=[blue,red], stepsize=0.1)       ]));

 

>

 

>	R:=0.8; display( array([      DEplot(xphug, [ theta(t), v(t), x(t), y(t) ], t=0..10,

 

>	[[theta(0)=0, v(0)=2.5, x(0)=0, y(0)=4 ],           [theta(0)=0, v(0)=.8,  x(0)=0, y(0)=1 ]],

 

>	theta=-Pi/2..3*Pi, v=0..3, x=-1..6, y=0..7,         scene=[theta,v],

 

>	linecolor=[blue,red], stepsize=0.1, title="v,theta phase"),

 

>	DEplot(xphug, [ theta(t), v(t), x(t), y(t) ], t=0..10,

 

>	[[theta(0)=0, v(0)=2.5, x(0)=0, y(0)=4 ],           [theta(0)=0, v(0)=.8,  x(0)=0, y(0)=1 ]],

 

>	theta=-Pi/2..3*Pi, v=0..3, x=-1..6, y=0..7,         scene=[x,y], title="path of glider",

 

>	linecolor=[blue,red], stepsize=0.1)       ]));

 

>

 

>	R:=3; display( array([      DEplot(xphug, [ theta(t), v(t), x(t), y(t) ], t=0..10,

 

>	[[theta(0)=0, v(0)=2.5, x(0)=0, y(0)=4 ],           [theta(0)=0, v(0)=.8,  x(0)=0, y(0)=1 ]],

 

>	theta=-Pi/2..3*Pi, v=0..3, x=-1..6, y=0..7,         scene=[theta,v],

 

>	linecolor=[blue,red], stepsize=0.1, title="v,theta phase"),

 

>	DEplot(xphug, [ theta(t), v(t), x(t), y(t) ], t=0..10,

 

>	[[theta(0)=0, v(0)=2.5, x(0)=0, y(0)=4 ],           [theta(0)=0, v(0)=.8,  x(0)=0, y(0)=1 ]],

 

>	theta=-Pi/2..3*Pi, v=0..3, x=-1..6, y=0..7,         scene=[x,y], title="path of glider",

 

>	linecolor=[blue,red], stepsize=0.1)       ]));

 

>

 

>

 

>

 

>	guts:= [ theta(t), v(t), x(t), y(t) ], t=0..10,

 

>	[[theta(0)=0, v(0)=2.5, x(0)=0, y(0)=4 ],           [theta(0)=0, v(0)=.8,  x(0)=0, y(0)=1 ],           [theta(0)=0, v(0)=1,  x(0)=0, y(0)=3 ]],

 

>	theta=-Pi/2..3*Pi, v=0..3, x=-1..6, y=0..7,

 

>	linecolor=[blue,red, black], stepsize=0.1:

 

>

 

>	R:=0; display( array([      DEplot(xphug, guts,         scene=[theta,v],title="v,theta phase"),      DEplot(xphug, guts,         scene=[x,y],title="glider path")]));

 

>

 

>

 

>	guts:= [ theta(t), v(t), x(t), y(t) ], t=0..10,

 

>	[seq( [theta(0)=0, v(0)=1+i/10, x(0)=0, y(0)=i+.1 ], i=0..10)],

 

>	theta=-Pi/2..3*Pi, v=0..3, x=-1..6, y=0..13,

 

>	linecolor=[seq(COLOR(HUE,i/10),i=0..10)], stepsize=0.1:

 

>

 

>	R:=0; display( array([      DEplot(xphug, guts,         scene=[theta,v],title="v,theta phase"),      DEplot(xphug, guts,         scene=[x,y],title="glider path")]));

 

>