Very few researchers have attempted to describe a biomechanical model for numerical simulation of front and back somersaults, as performed on the trampoline (without twist). But there are exceptions – take for example Wojciech Blajer (Department of Mechanics, Institute of Applied Mechanics, Technical University of Radom, Poland) and Adam Czaplicki (Department of Biomechanics, Institute of Sport and Physical Education, Biała Podlaska, Poland), who in 2001 presented their findings in the Journal of Biomechanics, 34
‘Modeling and inverse simulation of somersaults on the trampoline’
“A mathematical model for the analysis of front and back somersaults on the trampoline was developed. It can be applied to the solution of inverse dynamics problem as well as to the direct dynamics simulation. The same governing equations are used for the flying phase of somersault – when the body rotates above the trampoline bed, and for the support phase – when the athlete touches the bed. The only exception is that in the support phase the reactions from the bed on the feet are involved.”
The paper is admirably illustrated (as above), and can be examined in full here
Note:
The team followed up their research with a later paper for Multibody System Dynamics, 2003, Volume 10, Number 3, Pages 289-312
Also see: The math(s) of boomerangs and skateboards.