Where I come from we call a back somersault from sitting on a bar a “leaf drop”. No doubt it has other names in other regions.
It’s not a competitive skill, but is good psychological preparation for future dismounts.
Once the kids can do leaf drop for “fun”, the flyaway seems less “scary”.
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From Mountain Shadows Gymnastics Camp, Okotoks, Alberta, Canada.
One gymnast does double back leaf drop. This is not recommended due to the risk of landing on the neck in the foam pit.