> with(plots,animate);

[Maple Math]

> animate([e/(1+e*sin(2*t)),t,t=0..2*Pi],e=-2..2,coords=polar,view=[-4..4,-4..4],numpoints=150,frames=30);

> animate([e/(1+e*sin(5*t)),t,t=0..2*Pi],e=-2..2,coords=polar,view=[-4..4,-4..4],numpoints=150,frames=30);

> animate([e/(1+e*sin(25*t)),t,t=0..2*Pi],e=-2..2,coords=polar,view=[-4..4,-4..4],numpoints=150,frames=30);

> animate([e/(1+e*sin(125*t)),t,t=0..2*Pi],e=-2..2,coords=polar,view=[-4..4,-4..4],numpoints=150,frames=30);

>