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Invariants
Calculation of invariants - matlab codeDescripción completa...
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Sandoval Roberto
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%Cálculo de Invariantes I (numérico) format compact compact; ; clear; clc T=[5 2 0; 2 2 0; 0 0 3] ; Tsqrd = T*T ; I_T = trace(T); II_T = 0.5*(I_T^2 ‐ trace(Tsqrd)); III_T = det(T); fprintf('Tensor fprintf('Tensor ') ') T fprintf('Primer fprintf('Primer Invariante I ') ') I_T fprintf('Segundo fprintf('Segundo Invariante I') I') II_T fprintf('Tercer fprintf('Tercer Invariante I ') ') III_T %Cálculo de Invariantes I (literal) syms a b c d e f g h i A = [a b c; d e f; g h i]; Asqrd = A*A ; I_A = trace(A); II_A = 0.5*(I_A^2 ‐ trace(Asqrd)); II_A = simplify(II_A); III_A = det(A); fprintf('Tensor fprintf('Tensor ') ') A fprintf('Primer fprintf('Primer Invariante I ') ') I_A fprintf('Segundo fprintf('Segundo Invariante I ') ') II_A fprintf('Tercer fprintf('Tercer Invariante I ') ') III_A %Cálculo de Invariantes J (numérico) J_T = I_T ; JJ_T = 0.5*(I_T^2+2*II_T); JJJ_T = (1/3)*(I_T^3+3*I_T*II_T+3*III_T); fprintf('Tensor fprintf('Tensor ') ') T fprintf('Primer fprintf('Primer Invariante J ') ') J_T fprintf('Segundo fprintf('Segundo Invariante J ') ') JJ_T fprintf('Tercer fprintf('Tercer Invariante J ') ') JJJ_T %Cálculo de Invariantes J (literal) J_A = I_A ; JJ_A = 0.5*(I_A^2 ‐ 2*II_A); JJJ_A = (1/3)*(I_A^3+3*I_A*II_A+3*III_A); fprintf('Tensor fprintf('Tensor ') ') A fprintf('Primer fprintf('Primer Invariante J ') ') J_A fprintf('Segundo fprintf('Segundo Invariante J ') ') JJ_A fprintf('Tercer fprintf('Tercer Invariante J ') ') JJJ_A
Tensor T = 5 2 0 2 2 0 0 0 3 Primer Invariante I I_T = 10 Segundo Invariante III_T =
27 Tercer Invariante I III_T = 18 Tensor A = [ a, b, c] [ d, e, f] [ g, h, i] Primer Invariante I I_A = a + e + i Segundo Invariante I II_A = a*e ‐ b*d + a*i ‐ c*g + e*i ‐ Tercer Invariante I III_A = a*e*i ‐ a*f*h ‐ b*d*i + b*f*g Tensor T = 5 2 0 2 2 0 0 0 3 Primer Invariante J J_T = 10 Segundo Invariante J JJ_T = 77 Tercer Invariante J JJJ_T = 621.3333 Tensor A = [ a, b, c] [ d, e, f] [ g, h, i] Primer Invariante J J_A = a + e + i Segundo Invariante J JJ_A = b*d ‐ a*e ‐ a*i + c*g ‐ e*i + Tercer Invariante J JJJ_A = ((3*a + 3*e + 3*i)*(a*e ‐ b*d
Published with MATLAB® R2014a
f*h + c*d*h ‐ c*e*g
f*h + (a + e + i)^2/2 + a*i ‐ c*g + e*i ‐ f*h))/3 + (a + e + i)^3/3 + a*e*i ‐ a*f*h ‐ b*d*i + b*f*g + c*d*h ‐ c*e*g
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