Creating an Animation

Basically all animations in Mathematica consist of a sequence of plots which when rendered in rapid succession give the appearance of motion. The easiest way to create an animation is to use the Table function. Here is an example using two dimensional graphics.

2-D Example

Creating the plots

First we evaluate the following cell. Note the inclusion of "i" in the argument to the Sin function. This is used to create the appearance of motion by shifting the plot a little further to the left for each value of i. This will create a sequence of plots.

animation1  =  
      Table[Plot[Sin[x  +  2 i π/24], {x, 0, 2 π}], {i, 1, 
          24}]

Viewing the animation

To view the above animation we select the second cell bracket (counting from the left) and double-click. This will collapse all of the cells in the plot to a single cell. Now, leaving that cell bracket selected you can use the Cell/Animate Selected Graphics command from the Cell menu or use the keyboard shortcut listed there.

3-D Example

To create the kind of animation suggested by your original notebook we use some of the Graphics packages. We start by loading the packages.

<< Graphics`

Next we generate the form we want to rotate.

aa  =  
      SurfaceOfRevolution[Sin[x], {x, -π, π}, 
        RevolutionAxis  ->  {1, 0, 0}, Boxed  ->  False, 
        Axes  ->  False]

Now we find the ViewPoint for our plot.

AbsoluteOptions[aa, ViewPoint]

Now the idea is to create a sequence of ViewPoints which circle around the plot maintaining the same distance from the plot.

dist  =  (Sqrt[(1.3^2) + (2.4^2)])

Next we use the Table function to create a series of plots with different ViewPoints. The option SphericalRegion is used to maintain the size of the plot.

Table[
      Show[aa, ViewPoint ->  {dist Cos[t], dist Sin[t], 2}, 
        PlotRange  ->  {{- π,  π}, {- π,  π}, {-1, 1}}, SphericalRegion  ->  True], {t, π/12, 
        2 π, π/12}]

Viewing the Animation

We can view the animation the same way we did for the 2-D case. We can control the speed and direction of the animation using the controls that appear on the lower left of the notebook when we start the animation.