### newtonian mechanics - Model/formula for bouncing ball ...

In reality, as the ball deforms more, the spring constant will increase - which will actually make the contact time shorter as the impact velocity is higher. But for your simulation that is unlikely to matter. To get from the above to a "mathematical model" you might want to modify this python code to your needs:

You say you are ignoring friction of the air, but assume a partially inelastic collision. That means we can break the problem into two parts: While...2Well the difficulty is when the ball in contact with wall. Few things you can consider. elastic impact. In this case, you can treat the ball as an...0Visual Solutions (Now Altair) makes VisSim Software. Here is a demo block diagram that they have used to simulate a bouncing ball: The $1/s$ blocks...[PDF]