% rotating_vector plots a time-dependent point and vector 
%  following problem 7.2.4 in "Basic Training in Mathematics" 
%  by R. Shankar.
% 

% Programmer: Dick Furnstahl  furnstahl.1@osu.edu
%
% Revision history:
%   01-May-2005 -- original version for Physics 263
%
clear; clf;         % clear variables and figures

omega = 1;          % set the frequency

t_start = 0.0;      % starting time
t_end = 10.0;       % ending time
delta_t = 0.1;      % time between points plotted

% set up a vector from t_start to t_end spaced by delta_t
t = t_start : delta_t : t_end;  
x = cos(omega*t);      % evaluate at all t points
y = sin(omega*t);      % evaluate at all t points

% use a for loop to step through the time points one-by-one
for t0 = t_start : delta_t : t_end
   x0 = cos(omega*t0);     % the current x position
   y0 = sin(omega*t0);     % the current y position
   
   vx0 = -omega*sin(omega*t0);  % ???
   vy0 = omega*cos(omega*t0);   % ???
   
   plot(x0,y0,'ro');       % plot the current point with a red circle ('ro')
   axis([-1.5 1.5 -1.5 1.5]); axis square;   % set the axis dimensions
   hold on;                % hold the plot so we can add more plots

   scale = 1.0;   % scale factor for vectors
   % quiver will plot a vector based at x0,y0 with x and y
   %  components vx0,vy0, scaled by scale, in red ('r')
   quiver(x0,y0,vx0,vy0,scale,'r');  
   
   plot(x,y,'b');     % plot the entire trajectory in blue ('b')
   
   hold off;      % release the hold
   pause(.1);     % pause this fraction of a second    
end