I.N.E.R.T.I.A.

I.N.E.R.T.I.A. (Inertial Navigation Experience Reaction Test Inside Arena) is a simple one-on-one shooting game relying on fast reflexes and the proper use of inertia. You and a friend control two spaceships trapped inside an arena, where they bounce against the walls. Try to hit your bouncing opponent with as many shots as possible, and the one whose energy is depleted first is the winner. Speed and energy can be tuned in the game menu.

If you care about contrived background stories for shmups, apparently this game simulates a training chamber for pilots who must repel an upcoming attack by aliens.