I have a question for anyone who knows a lot about muscle anatomy. I need the name of the leg muscles involved in a kick when the leg is pulled back after extension. I am also looking for suggestions on how to train these and increase kick retraction speed for multiple kicks

Ideas anyone?

He Ill Cho has books with some pretty good anatomic layouts for kicking you could look into, called The Complete Master's Kick and The Complete Master's Jumping Kick.

An author by the name of Shawn Kovacich also has a series of books on kicking, each book being "kick specific," with some anatomical layouts in them, as well. I have a few of his books, and I like them.

I would say the key to learning to kick the way you are talking about is to use a chair or wall for balance, and do some slower, smooth kicking. Build those muscles up, and gain speed as you go.