MATLAB: Find the derivative of a piecewise function and plot the result

derivativefunctionpiecewise

Hi, I have the following code which includes a piecewise function "s" of theta and I would like to differentiate this function with respect to theta and plot the result after.

 L = 2.5;
 betha1 = 50*pi/180;
 betha2 = 260*pi/180;
 curv_arm = @(theta) L/2*(1-cos((pi*(theta-betha1))/betha1));
 curv_par = @(theta) L*(1-(theta-(100*pi/180))/(betha2)+((1)/(2*pi))*(sin(2*pi*(theta-(100*pi/180))/(betha2))));
 syms theta
 s = @(theta) [0*((0<theta) & (theta<50*pi)) + curv_arm(theta).*((50*pi/180<theta) & (theta<100*pi/180)) + 
 curv_par(theta).*((100*pi/180<theta) & (theta<2*pi))];
 fplot(s, [0,6], 'b')

I have managed to plot the current function but I can't differentiate with the command diff for some reason

Best Answer

The Symbolic Math Toolbox diff function will not differentiate it because of the discontinuities, either using my function or your original symbolic function for ‘s’. (The derivative does not exist at the discontinuities.)

The best you can do is to evaluate it numerically over a suitably fine vector for ‘theta’ (use the linspace function) and then use the gradient function to calculate the numerical derivative.

Then you can plot both the function and its numerical derivative as functions of ‘theta’.

Related Solutions

MATLAB: How to find the maximum and minimum values of a piecewise function

I’m not quite sure what you want to do. This will get you started:

curv_arm = 3;
curv_par = 5;
s = @(theta, curv_arm, curv_par) [0*((0<theta) & (theta<50*pi)) + curv_arm.*((50*pi/180<theta) & (theta<100*pi/180)) + curv_par.*((100*pi/180<theta) & (theta<2*pi))];
[x,fval] = fminbnd(@(theta)s(theta, curv_arm, curv_par),0,pi)

You cannot use a symbolic expression with fminbnd, and ‘matlabFunction’ will not create a function from your piecewise function. You can easily create your own function for numeric applications using essentially the same code, and ‘logical indexing’, as I did here.

Make any necessary changes to get the result you want.

MATLAB: Solving non linear equation using fsolve

You are not passing theta_n and other parameters to root2d(). One fix is to make root2d a Nested Function. Also, you must choose a different initial point. phi0 = [10,10] worked for me.

function solve_it()
    beta_a = 10;
    alpha_n = 10 ;
    eta= 18;
    i = 18;
    theta_i = 10;
    theta_n = 10 ;
    
    fun = @root2d;
    phi0 = [10,10];
    phi = fsolve(fun,phi0);
    phi_n = phi(1),
    phi_i = phi(2),
    function F = root2d(phi)
    F = zeros(2,1);
    F(1) = (pi*sin((pi*(phi(1) + theta_n))/180)*cos((pi*phi(2))/180)*(cos((pi*theta_n)/180) + tan((pi*i)/180)*tan((pi*theta_i)/180)))/(180*sin((pi*phi(1))/180)*(cos((pi*(phi(1) + theta_n))/180)*cos((phi(2)*pi)/180) + sin((phi(2)*pi)/180)*tan((theta_i*pi)/180))^2) - (pi*cos((pi*phi(1))/180)*(cos((pi*theta_n)/180) + tan((pi*i)/180)*tan((pi*theta_i)/180)))/(180*sin((phi(1)*pi)/180)^2*(cos((pi*(phi(1) + theta_n))/180)*cos((pi*phi(2))/180) + sin((pi*phi(2))/180)*tan((pi*theta_i)/180)));
    F(2) = ((cos((pi*theta_n)/180) + tan((pi*i)/180)*tan((pi*theta_i)/180))*((pi*cos((pi*(phi(1) + theta_n))/180)*sin((pi*phi(2))/180))/180 - (pi*cos((pi*phi(2))/180)*tan((pi*theta_i)/180))/180))/(sin((pi*phi(1))/180)*(cos((pi*(phi(1) + theta_n))/180)*cos((phi(2)*pi)/180) + sin((phi(2)*pi)/180)*tan((theta_i*pi)/180))^2);
    end
end

Best Answer

Related Solutions

MATLAB: How to find the maximum and minimum values of a piecewise function

MATLAB: Solving non linear equation using fsolve

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