In the opening to Shakespeare's Henry V, the Prologue refers to the theatre as "this cockpit"; why is the word "cockpit" used?

The Globe Theatre, where the play was originally performed, was nicknamed "The Wooden O" on account of its shape and the material from which it was made. This gave it the appearance of a giant cockpit, a place where cock fights would take place. Moreover, cockpit also refers to "The Pit," which was the area surrounding the stage of the Globe Theatre, where ordinary folk called "groundlings" could stand and watch a play for just a penny.
Fighting of a rather different kind is depicted in Henry V, which of course revolves around the Battle of Agincourt:

But pardon, gentles all,
The flat unraisèd spirits that hath dared
On this unworthy scaffold to bring forth
So great an object. Can this cockpit hold
The vasty fields of France? Or may we cram
Within this wooden O the very casques
That did affright the air at Agincourt?

In this excerpt from the prologue, Shakespeare's trying to fire the imagination of the audience. He wants them to forget their immediate surroundings in the theater and imagine that they are right there, along with Henry and his army, at the Battle of Agincourt.