title: Animate the movement of a point along the plot of a specific solution obtained using ParametricPlot3D
body: <p>We have the system: </p>
  
  <pre><code>x'[t] == x[t] - 5 y[t] + z[t]
  y'[t] == 3 x[t] - 3 y[t] - 3 z[t]
  z'[t] == -2 x[t] + 10 y[t] + 4 z[t]
  </code></pre>
  
  <p>and the initial conditions:</p>
  
  <pre><code>x[0] == .01
  y[0] == 3
  z[0] == 0
  </code></pre>
  
  <p>I produced the specific plot:</p>
  
  <pre><code>eqn = {x'[t] == x[t] - 5 y[t] + z[t],  y'[t] == 3 x[t] - 3 y[t] - 3 z[t], 
  z'[t] == -2 x[t] + 10 y[t] + 4 z[t]}; 
  
  sol = NDSolve[{eqn, x[0] == .01, y[0] == 3, z[0] == 0}, {x[t], y[t], 
  z[t]}, {t, -5, 5}]
  
  {xde[t_], yde[t_], zde[t_]} = {x[t], y[t], z[t]} /. Flatten[sol]
  
   ParametricPlot3D[{xde[t], yde[t], zde[t]}, {t, 0, 10}, 
   AxesLabel -&gt; {"x", "y", "z"}, 
   PlotRange -&gt; {{-15, 15}, {-15, 15}, {-15, 15}}]
  </code></pre>
  
  <p>I know how when pick a random point to plot the whole trajectory, but I can't find a way to animate a point moving along the trajectory that was plotted.
  In this particular example the point should be at t == 0 and move along until t == 2.</p>