Real life physics question - gymnastics

[calcbandit]

I am a junior mechanical engineering major and consider myself decent at understanding forces and moments and why things move.

I also used to do gymnastics, competitively, for 10 years.

I do not understand the physics behind twisting. I could do it myself, gymnasts are instructed to pull their hands upwards and to the side during a flip to acheive a twist.

Since the gymnast starts the flip with no angular momentum about the twisting axis (from bottom of feet through head), and end up twisting, some moment must have been applied to them to provide this angular momentum.

At first, I thought that this moment was applied from the floor mat as they took off for the flip, or perhaps from the high bar as they let go. However, this does not make sense, since it is possible and commonly done to do 2 flips in the air, the first one with no twist and the second one with twist (this is called a back in, full out). How did they suddently attain angular momentum while in the air between the first and second flips?