ME3255_HW4_mininumPE.m

%ME3255
%Homework 4
%Find minimum stuff

theta = 0;
x_l = 0;
x_u = 10;

%b) test collar_potential_energy
U_min = goldmin(@(x) collar_potential_energy(x, theta), x_l, x_u);

%c) find x_min for theta = 0 to 90
theta_u = degtorad(90); %upper limit of theta
theta = linspace(0, theta_u); %values of theta in radians;

%loop through values
for i = 1:length(theta)
	[x_min(i), U_min(i)] = goldmin(@(x) collar_potential_energy(x, theta(i)), x_l, x_u);
end

plot(U_min, theta);

%formatting chart
title('Minimum PE vs. theta');
ylabel('Total U (J)');
xlabel('theta (rad)');

xticks([0, pi/16, pi/8, 3*pi/16])
xticklabels({'0','\pi/16', '\pi/8', '\pi/16'}) %yay Tex!

print('minPEplot.png', '-dpng');