The diver with a rotor

Abstract

Abstract. We present and analyse a simple model for the twisting somersault. The model is a rigid body with a rotor attached which can be switched on and off. This makes it simple enough to devise explicit analytical formulas whilst still maintaining sufficient complexity to preserve the shape-changing dynamics essential for twisting somersaults in springboard and platform diving. With "rotor on" and with "rotor off" the corresponding Euler-type equations can be solved, and the essential quantities characterising the dynamics, such as the periods and rotation numbers, can be computed in terms of complete elliptic integrals. Thus we arrive at explicit formulas for how to achieve a dive with m somersaults and n twists in a given total time. This can be thought of as a special case of a geometric phase formula due to Cabrera [2].

Research on Body Type Correction of FINA Diving Difficulty Coefficient Based on Rigid Body System

“…Based on the above analysis, this study will establish a two-body as a theoretical model, in which the change of the moment of inertia I and the change of the angular momentum A are detailed in Bharadwaj et al [23].…”

Analogies of the classical Euler top with a rotor to spin squeezing and quantum phase transitions in a generalized Lipkin-Meshkov-Glick model

“…Relevant problems include rotational stabilization of rigid bodies [12][13][14] with applications to attitude control of spacecraft by momentum wheels. Recently, such a model has been used to analyze motion of a diver exerting a twisted somersault [15]: the body of the diver is modeled by an asymmetric top and the moving arms by a rotating disc.…”

A New Twisting Somersault: 513XD

“…Coaches are now seeking to better understand the biomechanics behind the aerial manoeuvres associated with a good dive to equip their athletes with a leading edge in competition. The purpose of this paper is to use the newly established mathematical framework developed in [4,6,17] to present the innovative 513XD 1 dive consisting of 1.5 somersaults and 5 twists that in principle can be performed by world class athletes. In doing so, we develop a mathematical understanding of the effects of shape change on the dynamics of the system.…”

“…Since then, Yeadon has extensively analysed aerial movement of the human body in [19,20,21,22] and the biomechanics of the twisting somersault in [23,24,25,26]. The simplest mechanism for producing the effect of twisting somersault is found in [4], which uses a rotor instead of arms to initiate and terminate twist. As the shape is not physically changing, the system is simple enough so that an analytical formula can be established connecting the number of somersaults, twists and airborne time.…”