Soreyuke! Uchuu Senkan Yamamoto Youko (1999)

In the year 2999: humanity is split into two factions, Terra and Ness, in a war fought by starships. One of the foremost of the pilots is the cocky teenager Yamamoto Yohko, and during one of her missions, she and her crew are sucked into a temporal anomaly (a la Star Trek) that sends her back to our time. Amnesiac, she only thinks of herself as a typical high school student - until a course of events sends her back to her ship the TA-29, with her newfound friends fighting at her side in a war that looks suspiciously like an arcade game (complete with 100 yen ignition costs!).
(Source: AniDB)