Undamped Pendulum Model

>	restart; with(DEtools):with(plots):

Warning, the name changecoords has been redefined

>	odes := diff(x(t),t)=y(t), diff(y(t),t) = -sin(x(t));

>	DEplot([odes],[x(t),y(t)],t=0..9,[[x(0)=.7,y(0)=0],[x(0)=-.7,y(0)=4]],x=-5..5,y=-5..5,arrows=SLIM, title="Undamped Pendulum",linecolor=blue);

>	DEplot([odes],[x(t),y(t)],t=0..9,[[x(0)=.7,y(0)=0],[x(0)=-.7,y(0)=4]],x=-5..5,y=-5..5,arrows=SLIM, title="Undamped Pendulum",linecolor=blue,scene=[t,x]);

Look at implicit plot of phase plane curves.

>	implicitplot(y^2/2-cos(x)=.7,x=-4..4,y=-3..3);

>	DEplot3d([odes],[x(t),y(t)],t=0..9,[[x(0)=.7,y(0)=0]],x=-5..5,y=-5..5,arrows=SLIM, title="Undamped Pendulum",linecolor=blue,scene=[t,x(t),y(t)]);

>