applying while loop for solving simultaneous equations
1 view (last 30 days)
Show older comments
I am trying to include a condition that 'tan(alphac)<(1/lam)' in the following code. Here, ''alphac'' is dependent of ''x''. and the value of x is determined at last. I want to write a code such that the value of x is determined by applying the condition.
code:
dbstop if error
clear all
clc
format longEng
syms x y lam
a=[4;0.55];
% The Newton-Raphson iterations starts here
LAM=linspace(0,10,11);
h=4;
q=20;
gma=18.4; nq=2*q/(gma*(h+x));
delta=26;
phi=39;
A=lam*nq/(1+nq);
kv=0;
kh=0;
da1=delta*(pi/180); da2=-delta*(pi/180); pha1=phi*(pi/180); pha2=phi*(pi/180);
dp1=delta*(pi/180); dp2=delta*(pi/180); php1=phi*(pi/180); php2=phi*(pi/180);
psi=atan(kh/(1-kv));
m=pha1+da1;
b=pha1-psi;
c=psi+da1;
alphac=atan((sin(m)*sin(b)+(sin(m)^2*sin(b)^2+sin(m)*cos(m)*sin(b)*cos(b)+A*cos(c)*cos(m)*sin(b))^0.5)/(A*cos(c)+sin(m)*cos(b)))
kg=(tan(alphac-pha1)+(kh/(1-kv)))/(tan(alphac)*(cos(da1)+sin(da1)*tan(alphac-pha1)));
r=1-lam*tan(alphac);
kq=r*kg;
A2=0;
alphac2=atan((sin(m)*sin(b)+(sin(m)^2*sin(b)^2+sin(m)*cos(m)*sin(b)*cos(b)+A2*cos(c)*cos(m)*sin(b))^0.5)/(A2*cos(c)+sin(m)*cos(b)))
kg2=(tan(alphac2-pha1)+(kh/(1-kv)))/(tan(alphac2)*(cos(da1)+sin(da1)*tan(alphac2-pha1)));
pg=0.5*gma*(1-kv)*kg2*(h+x)^2;
A=1;
alphac1=atan((sin(m)*sin(b)+(sin(m)^2*sin(b)^2+sin(m)*cos(m)*sin(b)*cos(b)+A*cos(c)*cos(m)*sin(b))^0.5)/(A*cos(c)+sin(m)*cos(b)))
kg1=(tan(alphac1-pha1)+(kh/(1-kv)))/(tan(alphac1)*(cos(da1)+sin(da1)*tan(alphac1-pha1)));
r1=1-lam*tan(alphac1);
kq1=r1*kg1;
pq=(1-kv)*(q*kq*(h+x)+0.5*q*(kq1-kq)*(h+x));
va2=asin(sin(da2)/sin(pha2))-asin(sin(psi)/sin(pha2))-da2-psi;
ka2=(1/cos(psi))*(cos(da2)*((cos(da2)-sqrt(sin(pha2)^2-sin(da2)^2)))/(cos(psi)+sqrt(sin(pha2)^2-sin(psi)^2)))*exp(-va2*tan(pha2));
vp1=asin(sin(dp1)/sin(php1))+asin(-sin(psi)/sin(php1))+dp1+psi;
kp1=(1/cos(psi))*(cos(dp1)*((cos(dp1)+sqrt(sin(php1)^2-sin(dp1)^2)))/(cos(psi)-sqrt(sin(php1)^2-sin(psi)^2)))*exp(vp1*tan(php1));
vp2=asin(sin(dp2)/sin(php2))+asin(-sin(psi)/sin(php2))+dp2+psi;
kp2=(1/cos(psi))*(cos(dp2)*((cos(dp2)+sqrt(sin(php2)^2-sin(dp2)^2)))/(cos(psi)-sqrt(sin(php2)^2-sin(psi)^2)))*exp(vp2*tan(php2));
sinda1=sin(da1); sindp1=sin(dp1); sinda2=-sin(da2); sindp2=sin(dp2);
cosda1=cos(da1); cosdp1=cos(dp1); cosda2=cos(da2); cosdp2=cos(dp2);
pp1=kp1*gma*0.5*(x^2);
pa2=ka2*gma*(x*y+0.5*(y^2)); pp2=kp2*gma*(y*(h+x)+(0.5*(y^2)));
zp1=x/3;
zp2=((0.5*(h+x)*(y^2))+((y^3)/3))/(((h+x)*y)+(0.5*(y^2)));
za2=((0.5*x*(y^2))+((y^3)/3))/((x*y)+(0.5*(y^2)));
e2=(pp1*cosdp1)+(pa2*cosda2)-(pg*cosda1)-(pp2*cosdp2)-pq;
e3=(pp1*cosdp1*zp1)+(pp2*cosdp2*zp2)-(pg*cosda1*((h+x)/3))-(pa2*cosda2*za2)-pq*(1/3)*(h+x)*((kq+2*kq1)/(kq+kq1));
g=[e2; e3];
J=jacobian([e2, e3], [x, y]);
A=zeros(2,numel(LAM));
for i=1:numel(LAM)
del=1;
indx=0;
lam=0;
while del>1e-6 && tan(alphac)<(1/lam)
gnum = vpa(subs(g,[x,y,lam],[a(1),a(2),LAM(i)]));
Jnum = vpa(subs(J,[x,y,lam],[a(1),a(2),LAM(i)]));
delx = -Jnum\gnum;
a = a + delx;
del = max(abs(gnum));
indx = indx + 1;
end
Z(:,i)=double(a)
end
0 Comments
Answers (0)
See Also
Categories
Find more on Calculus in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!