Laboratorios de Maple Geometr\355a Diferencial MATE2410 Prof. Jos\351 Ricardo ARTEAGA BEJARANO
Lab2-cont:Curvaturas de Superficies<Text-field layout="Heading 1" style="Heading 1"><Font encoding="ISO8859-1">C\341lculo de las Curvaturas</Font></Text-field><Text-field layout="Heading 2" style="Heading 2">Formulas</Text-field>retart: with(plots): with(LinearAlgebra):EFG:=proc(X)
local Xu,Xv,E,F,G;
Xu:=<diff(X[1],u),diff(X[2],u),diff(X[3],u)>;
Xv:=<diff(X[1],v),diff(X[2],v),diff(X[3],v)>;
E:=DotProduct(Xu,Xu,conjugate=false);
F:=DotProduct(Xu,Xv,conjugate=false);
G:=DotProduct(Xv,Xv,conjugate=false);
simplify([E,F,G]);
end:UN:=proc(X)
local Xu,Xv,Z,s;
Xu:=<diff(X[1],u),diff(X[2],u),diff(X[3],u)>;
Xv:=<diff(X[1],v),diff(X[2],v),diff(X[3],v)>;
Z:=CrossProduct(Xu,Xv);
s:=VectorNorm(Z,Euclidean,conjugate=false);
simplify(<Z[1]/s|Z[2]/s|Z[3]/s>,sqrt,trig,simbolic);
end:lmn:=proc(X)
local Xu,Xv,Xuu,Xuv,Xvv,U,l,m,n;
Xu:=<diff(X[1],u),diff(X[2],u),diff(X[3],u)>;
Xv:=<diff(X[1],v),diff(X[2],v),diff(X[3],v)>;
Xuu:=<diff(Xu[1],u),diff(Xu[2],u),diff(Xu[3],u)>;
Xuv:=<diff(Xu[1],v),diff(Xu[2],v),diff(Xu[3],v)>;
Xvv:=<diff(Xv[1],v),diff(Xv[2],v),diff(Xv[3],v)>;
U:=UN(X);
l:=DotProduct(U,Xuu,conjugate=false);
m:=DotProduct(U,Xuv,conjugate=false);
n:=DotProduct(U,Xvv,conjugate=false);
simplify([l,m,n],sqrt,trig,symbolic);
end:MK:=proc(X)
local E,F,G,l,m,n,S,T;
S:=EFG(X); T:=lmn(X);
E:=S[1]; F:=S[2]; G:=S[3];
l:=T[1]; m:=T[2]; n:=T[3];
simplify((G*l+E*n-2*F*m)/(2*E*G-2*F^2),sqrt,trig,symbolic);
end:GK:=proc(X)
local E,F,G,l,m,n,S,T;
S:=EFG(X); T:=lmn(X);
E:=S[1]; F:=S[2]; G:=S[3];
l:=T[1]; m:=T[2]; n:=T[3];
simplify((l*n-m^2)/(E*G-F^2),sqrt,trig,symbolic);
end: