| MadSci Network: Physics |
If you are asking for a nice, simple equation for such a trajectory, you'll
be very disappointed. (I was) On the other hand, I do like complex
problems...
I think you're interested in this situation:
height h
^
:
: xxxxxx -
: xx xxx ---
: ----- x BALL xx ------ ---
: ---- xxx xx ---- ---- ---
: ---- xxxxx ----- ------
: ----------- bumpy ground
:
O------------------------------------> position x
The ball (labelled "BALL") is rolling over a bumpy ground. As I've drawn
it, the ball can only go up, down, forward, or backward and the ground is
relatively smooth (the bumps are not sharp). In this case, if I gave you a
formula for the height "h" of the ground as a function of position "x".
h = f(x)
Then you could derive a formula for the ball's motion as a function of
time, given where the ball starts and how fast it's moving.
If the bumps in the ground are sharp bumps, then the problem is much more
difficult, for the ball may skip or slip. Then, your formula for the
ball's motion as a function of time will be complicated.
If the sharp-bumpy ground is two-dimensional, i.e. if the ball can move
forward, backward, and sideways, then the formulae for the balls motion
will probably be too much for you. You'll want to use a computer.
The subject that you're asking about is known academically as "rigid body
dynamics" You really ought to get your hands on a textbook about the
subject. A librarian at your local university should be able to point you
in the right direction.
Troy.
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