> restart:
Ejercicio 6 - Examen final 11 septiembre 2000
José Mª Goicolea, septiembre 2000
Problema de cinemática 3D
> with(linalg):
Warning, the protected names norm and trace have been redefined and unprotected
> u:=vector([-cos(theta),0,sin(theta)]);
> j:=vector([0,1,0]);
> ju:=crossprod(j,u);
> AD:=evalm(a*cos(theta)*j+a*sin(theta)*ju);
> Omega:=vector([-omega/tan(theta),omega/sin(theta),omega]);
> thetad:=omega/sin(theta);
> Omegad:=evalm(map(diff,Omega,theta)*thetad);
> Omegad:=simplify(Omegad);
> map(simplify,Omegad,{1-cos(theta)^2=sin(theta)^2});
> v[AD]:=crossprod(Omega,AD,trig);
> v[AD]:=simplify(v[AD],trig);
> v[A]:=vector([0,0,diff(a*sin(theta),theta)*thetad]);
> v[D]:=evalm(v[A]+v[AD]);
> Omegan2:=simplify((Omega[1]^2+Omega[2]^2+Omega[3]^2));
> Omegan2:=simplify(Omegan2,{1-cos(theta)^2=sin(theta)^2});
> Omegan:=sqrt(Omegan2,symbolic);
> Omegan1:=evalm(Omega/Omegan);
> Omegan1:=map(simplify,Omegan1);
> v[min]:=simplify(dotprod(v[A],Omegan1),symbolic);