vector_calc_identiti.mw

Download vector_calc_identiti.mw

Download vector_calc_identiti.mw

Download vector_calc_identiti.mw

I am attempting a few experiments with rotated ellipses with MAPLE, ie- 5x^2+5y^2-5xy=1.My first upload must not have taken.

OK ainclude are my images of my derivation if I uploaded them correctly.

I found your input on this matter of roots very educational.  Unfortunately, I have a nastier expression that solves for eigenvalues of pressure & shear waves propagating along an interface between 2 elastic media.  There are many roots to this expression for eta, but many of them can be excluded because the material properties are both REAL & POSITIVE.  I am very new to MAPLE & I am attempting to get it to solve for the roots where all of the other parameters meet the conditions of REAL & POSITIVE but I am not sure I am doing this correctly because MAPLE runs off to evaluation mode & takes so much memory my computer slows to a crawl & I terminate the evaluation.  Do I need to be more patient or do you have suggestions where I can limit MAPLE to assess only for the cases I need.  My thoughts are that MAPLE is attepting to assess all possible roots & that may not even be feasible even for a MONSTER computer.  I have included my expression below:

eq := alpha^2*sqrt(1-(alpha*eta/kappa[B])^2)*((2-eta^2)^2-4*sqrt(1-(eta/kappa)^2)*sqrt(1-eta^2))+mu[B]*sqrt(1-(eta/kappa)^2)*((2-(alpha*eta)^2)^2-4*sqrt(1-(alpha*eta/kappa[B])^2)*sqrt(1-(alpha*eta)^2))/mu

I found your input on this matter of roots very educational.  Unfortunately, I have a nastier expression that solves for eigenvalues of pressure & shear waves propagating along an interface between 2 elastic media.  There are many roots to this expression for eta, but many of them can be excluded because the material properties are both REAL & POSITIVE.  I am very new to MAPLE & I am attempting to get it to solve for the roots where all of the other parameters meet the conditions of REAL & POSITIVE but I am not sure I am doing this correctly because MAPLE runs off to evaluation mode & takes so much memory my computer slows to a crawl & I terminate the evaluation.  Do I need to be more patient or do you have suggestions where I can limit MAPLE to assess only for the cases I need.  My thoughts are that MAPLE is attepting to assess all possible roots & that may not even be feasible even for a MONSTER computer.  I have included my expression below:

eq := alpha^2*sqrt(1-(alpha*eta/kappa[B])^2)*((2-eta^2)^2-4*sqrt(1-(eta/kappa)^2)*sqrt(1-eta^2))+mu[B]*sqrt(1-(eta/kappa)^2)*((2-(alpha*eta)^2)^2-4*sqrt(1-(alpha*eta/kappa[B])^2)*sqrt(1-(alpha*eta)^2))/mu