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Task/Animate-a-pendulum/MATLAB/animate-a-pendulum.m

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+%This is a numerical simulation of a pendulum with a massless pivot arm.
+
+%% User Defined Parameters
+%Define external parameters
+g = -9.8;
+deltaTime = 1/50; %Decreasing this will increase simulation accuracy
+endTime = 16;
+
+%Define pendulum
+rodPivotPoint = [2 2]; %rectangular coordinates
+rodLength = 1;
+mass = 1; %of the bob
+radius = .2; %of the bob
+theta = 45; %degrees, defines initial position of the bob
+velocity = [0 0]; %cylindrical coordinates; first entry is radial velocity,
+                  %second entry is angular velocity
+
+%% Simulation
+assert(radius < rodLength,'Pendulum bob radius must be less than the length of the rod.');
+
+position = rodPivotPoint - (rodLength*[-sind(theta) cosd(theta)]); %in rectangular coordinates
+
+%Generate graphics, render pendulum
+figure;
+axesHandle = gca;
+xlim(axesHandle, [(rodPivotPoint(1) - rodLength - radius) (rodPivotPoint(1) + rodLength + radius)] );
+ylim(axesHandle, [(rodPivotPoint(2) - rodLength - radius) (rodPivotPoint(2) + rodLength + radius)] );
+
+rectHandle = rectangle('Position',[(position - radius/2) radius radius],...
+    'Curvature',[1,1],'FaceColor','g'); %Pendulum bob
+hold on
+plot(rodPivotPoint(1),rodPivotPoint(2),'^'); %pendulum pivot
+lineHandle = line([rodPivotPoint(1) position(1)],...
+    [rodPivotPoint(2) position(2)]); %pendulum rod
+hold off
+
+%Run simulation, all calculations are performed in cylindrical coordinates
+for time = (deltaTime:deltaTime:endTime)
+
+    drawnow; %Forces MATLAB to render the pendulum
+
+    %Find total force
+    gravitationalForceCylindrical = [mass*g*cosd(theta) mass*g*sind(theta)];
+
+    %This code is just incase you want to add more forces,e.g friction
+    totalForce = gravitationalForceCylindrical;
+
+    %If the rod isn't massless or is a spring, etc., modify this line
+    %accordingly
+    rodForce = [-totalForce(1) 0]; %cylindrical coordinates
+
+    totalForce = totalForce + rodForce;
+
+    acceleration = totalForce / mass; %F = ma
+    velocity = velocity + acceleration * deltaTime;
+    rodLength = rodLength + velocity(1) * deltaTime;
+    theta = theta + velocity(2) * deltaTime; % Attention!! Mistake here.
+    % Velocity needs to be divided by pendulum length and scaled to degrees:
+    % theta = theta + velocity(2) * deltaTime/rodLength/pi*180;
+
+    position = rodPivotPoint - (rodLength*[-sind(theta) cosd(theta)]);
+
+    %Update figure with new position info
+    set(rectHandle,'Position',[(position - radius/2) radius radius]);
+    set(lineHandle,'XData',[rodPivotPoint(1) position(1)],'YData',...
+        [rodPivotPoint(2) position(2)]);
+
+end