with(plots);<Text-field layout="Heading 1" style="Heading 1">I - Calcul d'enveloppe : La biellette de longueur a>0.</Text-field>E1 := x/(a*cos(t))+y/(a*sin(t))-1;
E1 := convert(E1,tan);
E1 := subs(tan(t/2)=u,E1);
E1 := E1*(1-u^2)*u;
E1 := simplify(E1);E2 := x*sin(t)^3-y*cos(t)^3;
E2 := convert(E2,tan);
E2 := subs(tan(t/2)=u,E2);
E2 := E2*(1+u^2)^3;
E2 := simplify(E2);solve({E1,E2});
EE1 := subs(a=1,E1); EE2 := subs(a=1,E2);
solve({EE1,EE2});
sol := [op(2,solve({EE1,EE2})[4][2]),op(2,solve({EE1,EE2})[4][3])];
plot([sol[1](u),sol[2](u),u=0..1]);<Text-field layout="Heading 1" style="Heading 1"> II - Calcul d'enveloppe : La biellette de longueur a>0.</Text-field>Enveloppe : u,v,w en t => equation parametrique de l'enveloppe.enveloppe := proc(u,v,w,t)
local du,dv,dw,delta;
du := diff(u,t);
dv := diff(v,t);
dw := diff(w,t);
delta := dv*u-v*du;
RETURN([(v*dw-dv*w)/delta,(du*w-u*dw)/delta]);
end;
echelle := proc(a)
RETURN(enveloppe(1/(a*cos(t)),1/(a*sin(t)),-1,t));
end;E := echelle(1);F1 := u->subs(t=u,E[1]);F2:=u->subs(t=u,E[2]);plot([F1,F2,0..Pi/2]);echelleplot := proc(alpha,n)
local Droites,i;
Droites := {};
for i from 1 to n do
Droites := Droites union {subs(t=Pi/2*i/(n+1),x/(alpha*cos(t))+y/(alpha*sin(t))-1)};
od;
implicitplot(Droites,x=0..alpha,y=0..alpha);
end;
echelleplot(1,50);