MATLAB: Integration in matlab: Explicit integral could not be found

integration

H=1,R=1,theta=20;
syms x;
syms alpha;
%sigma=F/(2*pi*R*(alpha-1));
z_desh=((x/alpha*x^2+1-alpha)^2-1)^-.5
beta=(sin(theta)+(sin(theta)*sin(theta)+4*alpha*(alpha-1)))/2*alpha
eq=int(z_desh,x,4,1)
when i run the above code en error show like: Warning: Explicit integral could not be found. How to solve this.? 
Thanks

Best Answer

First thing to do is heck whether the x/alpha*x^2 is really what you meant. If it was, why not say x^3/alpha ?

Next, check whether you really want to integrate from 4 down to 1, instead of from 1 to 4.

Thirdly, check why you define beta but then do not use it in what is being integrated.

If your integral is exactly as shown, then there is no readily available analytic form for it. A small number of values of alpha lead to analytic forms; the others do not.

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MATLAB: Is it so hard for MATLAB to solve the following symbolic equation

This seems to work

syms rp alpha beta theta psi z
A=cos(alpha)-cos(beta);
B=sin(alpha)-sin(beta);
C=(cos(beta)-1)/tan(beta)-(cos(alpha)-1)/tan(alpha);
R=A*(cos(theta)-cos(psi))+B*cos(theta)*sin(psi);
S=A*sin(theta)*sin(psi)-B*cos(theta)+C*cos(psi);
phi=atan(-R/S);
x=-rp*(cos(theta)*cos(phi)+sin(psi)*sin(theta)*sin(phi))*cos(alpha)-rp*(-cos(theta)*sin(phi)+sin(psi)*sin(theta)*cos(phi))*sin(alpha)+(rp/tan(alpha))*(cos(psi)*sin(phi)*(cos(alpha)-1)+cos(psi)*cos(phi)*sin(alpha));
y=-cos(psi)*sin(phi)*rp;
p=[x;y;z];
T=Rot('y',theta)*Rot('x',psi)*Rot('z',phi);
a1=T*[rp;0;0];
a2=T*[rp*cos(alpha);rp*sin(alpha);0];
a3=T*[rp*cos(beta);rp*sin(beta);0];  
Con1=(p+a1)'*[0;1;0];
Con2=(p+a2)'*[-sin(alpha);cos(alpha);0];
Con3=(p+a3)'*[-sin(beta);cos(beta);0];
disp([Con1; Con2; Con3])
function output=Rot(axis,angle)
syms x y z
if axis==x
    output=[1,0,0;0,cos(angle),-sin(angle);0,sin(angle),cos(angle)];
end
if axis==y
    output=[cos(angle),0,sin(angle);0,1,0;-sin(angle),0,cos(angle)];
end
if axis==z
    output=[cos(angle),-sin(angle),0;sin(angle),cos(angle),0;0,0,1];
end
end

MATLAB: How to define different color for all three plots

solution:

omega = 1; alpha = 1;beta=1;
f=@(ts,theta)[omega + alpha*(sin((theta(2)-theta(1))));
    omega + alpha*(sin(theta(1)-theta(2)))+beta*(sin(theta(3)-theta(2)));
omega + beta*(sin((theta(2)-theta(3))))];
range = [0,1];
thetainit = [0.1,0.3,0.2];
[range,theta] = ode45(f,range,thetainit);
h=plot(range,theta,'Linewidth', 2);
set(h,{'Color'},{'r'; 'g'; 'b'})
xlabel('Range');
ylabel('Theta');
legend('Theta1','Theta2','Theta3');

Best Answer

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MATLAB: Is it so hard for MATLAB to solve the following symbolic equation

MATLAB: How to define different color for all three plots

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