How to reverse the direction of bouncing ball equation?
The solution is detailed here:
http://reactorlab.net/resources-folder/matlab/pdf-link-folder/bouncing_ball_equations.pdf
In particular "Using the analytical solution for this case".
My problem. If I want to make the ball bounce off horizontal surfaces (e.g. top/bottom in box), then what do I need to adjust?
I've tried reversing the $+$ to $-$ by logic that the equation is basically:
start point + add something
so that the "add something" would define the curve, which goes "positive", because there's $+$. But this doesn't work. I cannot adjust gravity, because it doesn't make physical sense to adjust it. I cannot adjust $v_0$, because the reversing of direction is not related to an alteration in velocity (in this case).
Problem explanation:
Imagine that you want to make the particle bounce in a box in $\mathbb{R}^2$. For vertical directions one simply reverses the $x$: $x + \Delta x$ becomes $x - \Delta x$. But for horizontal?
Actually I noticed that it's described in the paper and it seems to work:
p. 2.
QUESTION
But why does one have to set $t=0$ at collision?