USS Teardrop NCC-75642
The USS Teardrop was originally commissioned as a standard Galaxy class starship and was among the second batch of the class to be constructed. At the time of launch, she utilized standard Isolinear controlled computer systems, subspace sensors and science facilities, and defenses. However, in response to a directive from Starfleet command to improve warp propulsion systems and make them safer, particularly after the discovery of the damage warp drives from that time caused to subspace, the Teardrop become the second of two Galaxy class vessels that became testbeds. The first vessel had been the USS Dragon, and the upgrades and experiments hadn't been as successful as R&D had hoped. In 2371, the Teardrop entered drydock and underwent modifications similar to that of the USS Dragon, including two additional nacelles placed on the underside and bioneural gel pack integration into the computer systems. The experiments were again not as big of a success as had been hoped, and the Galaxy class starship design had been deemed inefficient as far as warp fields were concerned. Even to this day, the warp five speed limit still applies to Galaxy class starships.
In 2379, the USS Teardrop came under the command of Captain Peter Andrews. Under his command, the ship fought in the final battle of the Kiklar War. During the battle the ship had become severely damaged and all hands were forced to abandon ship. One crew member had remained behind and had rammed the ship into an enemy vessel, thereby destroying it.
Despite how much I like the Galaxy class starships, I believe they are beginning to be phased out. Granted even in 2381 there will still be Galaxy class starships under construction, but the class's defenses and warp capabilities simply aren't up to par with the Sovereign class starship. Even the Intrepid class starship can outperform them in many ways. Their greatest advantages are the advanced research facilities and sensor packets, but they aren't as suited to multi-role tasks as the Sovereign class. I think they're already starting to become part of the work horses of the fleet, far more advanced than the aged Excelsior class to be sure, and they'll likely be on the frontiers of exploration for at least another decade. But assuming Starfleet isn't forced to enter another war in the near future, I think the Sovereigns will eventually be converted to more exploration-geared starships and the Galaxy classes will then have to find their own places in the Federation.
The Teardrop specifically was requested to cameo in STDragon by Star Trek Peacemaker's creator, Daniel Balding, to help link to the series together.