Physics/Logic behind self-bounce

What would a ball look like when it makes itself bounce. Say, for example that the ball had its own "inner power", was made out of (mostly) rubber, and pulled the top of itself inward and then released, causing itself to 'bounce' up. Is that logic correct? And is this what it would look like?

If this logic is correct, what other materials can have this effect given the scenario described above?

• I wouldn't worry too much about reality. A thing like this probably couldn't exist in the real world. Closest I can think of are half-ball shaped plastic 'poppers' you can get at toy stores. You poke them inside out and when they pop they bounce into the air. Maybe start there if you really want realism. Commented Dec 20, 2012 at 15:51
• Yes. I forgot about those. That is exactly the effect I am trying to achieve. Except with those, you push it inward, but in my game, the ball pulls the top of itself inward and then releases to jump up. Commented Dec 20, 2012 at 16:01
• Push inward, roll over, pop. :) Commented Dec 20, 2012 at 17:23

If I was the ball, I think I would try to 1. maximise the surface of contact with the ground and 2. maximise the vertical compression so that the release will generate forces that are normal to the ground:

In your example, a lot of the energy stored by the compression is lost: if the released surface does not touch or hit the ground, it'll just move air around.

However, I am also a great fan of Richard Williams's The Animator's Survival Kit, where one of the most valuable lessons is probably to focus more on the viewer's perception than on physical accuracy. Actually your animation may look a lot better if it's not physically accurate.

Here's an example from Williams; see how the 5th frame stretches the ball before touching the ground, for no physical reason:

So, my idea would be to go for the very simple vertical stretch (such as in this video), and add dramatic effects instead, such as causing the ball to shake and vibrate more and more as it squeezes itself. I suggest watching various animation examples frame to frame. There may also be good stuff in One Piece!