# Is the trajectory of a particle with constant velocity (though its direction can change by collisions) always non-chaotic?

Suppose we have a particle that travels with constant velocity, without heat losses by friction, and no forces acting on it except for occasionally collisions with much bigger wall-like masses than the particle (so that doesn't change the magnitude of its velocity but only its direction). Now, the trajectory of such a particle varies linearly when changing the direction of the velocity by a very small amount. The difference between the two trajectories increases linearly in time.

Is the movement of a particle with a constant velocity (without forces acting on it except at the "moments" it collides with a straight wall, without changing the magnitude of the particle's velocity) always non-chaotic (i.e. varying the initial direction of the particle's velocity gives a linear change in its trajectory) or are there cases that the particle's trajectory is chaotic? For example, if the heavy masses the particle collides with are not straight walls (like a particle moving inside a circular confinement). Or is the trajectory of a single particle (under the aforementioned conditions) always non-chaotic?

Any process that’s involving i.e. collisions with hard balls or sharp corners will have trajectories where a small displacement $\epsilon$ will make the difference between a hit or a miss. And the number of those, and the trajectory divergence they cause, grows with time.