In an equation, is that possible to give two uknowns'ratio expression by using "solve" function or other accessible way ?
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The equation is , is that possible to get "a/c" directly by "solve" function or other symbolic functions?
syms p p0 a r k alpha Y G
syms A B c d
sigma_re=-p0-B*r^(-(1+k));
sigma_thetae=-p0+B/k*r^(-(1+k));
sigma_rp=Y/(alpha-1)+A*r^(k*(alpha-1));
sigma_thetap=Y/(alpha-1)+A*alpha*r^(k*(alpha-1));
eqn1=subs(sigma_thetae,r,c)==subs(sigma_thetap,r,c);
eqn2=subs(sigma_re,r,c)==subs(sigma_rp,r,c);
[A1 B1]=solve([eqn1 eqn2],[A B]);
sigma_re=simplify(subs(sigma_re,B,B1),"IgnoreAnalyticConstraints",true)
sigma_thetae=simplify(subs(sigma_thetae,B,B1),"IgnoreAnalyticConstraints",true)
sigma_rp=simplify(subs(sigma_rp,A,A1),"IgnoreAnalyticConstraints",true)
sigma_thetap=simplify(subs(sigma_thetap,A,A1),"IgnoreAnalyticConstraints",true)
sigma_rp_a=simplify(subs(sigma_rp,r,a),"IgnoreAnalyticConstraints",true)
eqn3=sigma_rp_a==-p
2 Comments
Star Strider
on 11 Sep 2021
‘is that possible to get "a/c" directly by "solve" function or other symbolic functions?’
Please expand on this.
What result do you want?
.
Accepted Answer
Walter Roberson
on 11 Sep 2021
syms A B c d p p0 a r k alpha Y G
sigma_re=-p0-B*r^(-(1+k));
sigma_thetae=-p0+B/k*r^(-(1+k));
sigma_rp=Y/(alpha-1)+A*r^(k*(alpha-1));
sigma_thetap=Y/(alpha-1)+A*alpha*r^(k*(alpha-1));
eqn1=subs(sigma_thetae,r,c)==subs(sigma_thetap,r,c);
eqn2=subs(sigma_re,r,c)==subs(sigma_rp,r,c);
[A1 B1]=solve([eqn1 eqn2],[A B]);
sigma_re=simplify(subs(sigma_re,B,B1),"IgnoreAnalyticConstraints",true);
sigma_thetae=simplify(subs(sigma_thetae,B,B1),"IgnoreAnalyticConstraints",true);
sigma_rp=simplify(subs(sigma_rp,A,A1),"IgnoreAnalyticConstraints",true);
sigma_thetap=simplify(subs(sigma_thetap,A,A1),"IgnoreAnalyticConstraints",true);
sigma_rp_a=simplify(subs(sigma_rp,r,a),"IgnoreAnalyticConstraints",true)
syms c_a
temp = simplify(subs(sigma_rp_a, c, c_a*a))
output = simplify(solve(temp==-p,c_a,"IgnoreAnalyticConstraints",true))
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