MATLAB: How to derive an equation of Theta_a in terms of L_a using ‘solve’ command or any other way in Matlab

equationsolve

aIa=1;
bIa=aIa;
aIIa=1.25*aIa;
landaIa=pi/3;
landaIIa=acos((aIa*cos(landaIa))/aIIa); 
KIa=1;
Kca=KIa;
KIIa=20*KIa;
s1a=sin(landaIa);
t2a=tan(landaIIa);
t1a=tan(landaIa);
syms L_a theta_a
eqn1_a=aIa*s1a*((sqrt(((t2a^2)/(t1a^2))-((cos(theta_a).^2))))-sin(theta_a))-L_a==0;
g=solve(eqn1_a,L_a)

Best Answer

There appear to be two solutions:

 atan2(-(16*L_a^2-9)*sqrt(3)/(48*L_a), sqrt(-768*L_a^4+3168*L_a^2-243)/(48*L_a))
 atan2(-(16*L_a^2-9)*sqrt(3)/(48*L_a), -sqrt(-768*L_a^4+3168*L_a^2-243)/(48*L_a))

Found with Maple. MATLAB does not appear to be able to find this.

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MATLAB: How to solve a nonlinear non-transcendental equation numerically- I have a non-linear non-transcendental equation, I have tried vpasolve function but it does not provide correct roots, do you know how can I find the roots of such an equation? Thank

I tried this

clc,clear
c1 = 1;
c2 = 2;
c3 = 3;
L = 5;
syms landa
f = (c1-c2*landa^4)*((sinh(landa*L))^2 - (sin(landa*L))^2) - (c1-c2*landa^4)*(cosh(landa*L)+cos(landa*L))^2 + c3*(cosh(landa*L)-cos(landa*L))*(sinh(landa*L)+sin(landa*L)) - (cosh(landa*L)-cos(landa*L))*(sinh(landa*L)+sin(landa*L));
F = matlabFunction(f);
x = linspace(-1,1)/3;
y = F(x);
[~,ix] = min(abs(y));
plot(x,y,x(ix),y(ix),'*r')
grid on

result

MATLAB: Solving trigonometrique equation

You will never get an analytical result here.

vpasolve(g1)
ans =
-0.04489097131344154920928045475445

Best Answer

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MATLAB: How to solve a nonlinear non-transcendental equation numerically- I have a non-linear non-transcendental equation, I have tried vpasolve function but it does not provide correct roots, do you know how can I find the roots of such an equation? Thank

MATLAB: Solving trigonometrique equation

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