Dainis A
Med Sci Sports Exerc. 1981;13(1):34-43.
A mathematical model describing the motion of a gymnast represented by a planar three-segment link system is developed for the airborne and horse-support phases of vaulting. Four handspring vaults performed by advanced-level female gymnasts were analyzed and the results were used to verify the model. In order to describe observed performance, it was found necessary to consider the period of support on the vaulting horse as being comprised of two distinct phases: a compression phase and a repulsion phase. Solutions of the model are presented graphically enabling the relationships of important variables to be readily observed, and predictions to be made. Good agreement between observed performance and the model was obtained in all cases. The take-off velocity and initial distance from the horse were found to be the principal variables affecting the outcome of the vault. The model indicated that in the case of a good vault, a decrease of 7% in the take-off horizontal speed would cause a reduction of 13% in after-flight distance, and a similar decrease in the vertical speed would produce a 25% reduction in after-flight distance. Also, the force exerted by the performer during the repulsion phase has only a minimal effect on the after-flight characteristics of the vault. The take-off velocity requirements for an excellent vault were investigated for varying take-off distances from the horse. As the distance was decreased, the necessary velocity was decreased, but the angular velocity of the body required during the pre-flight phase was found to increase very rapidly.
针对跳马的空中阶段和支撑马阶段，建立了一个描述由平面三段连杆系统表示的体操运动员运动的数学模型。对高水平女子体操运动员进行的四个手翻跳马动作进行了分析，并将结果用于验证该模型。为了描述观察到的表现，发现有必要将支撑马的阶段视为由两个不同阶段组成：压缩阶段和推斥阶段。以图形方式展示了模型的解，使得重要变量之间的关系能够很容易地被观察到，并能进行预测。在所有情况下，观察到的表现与模型之间都取得了良好的一致性。发现起跳速度和离马的初始距离是影响跳马结果的主要变量。模型表明，在跳马表现良好的情况下，起跳水平速度降低7%将导致飞行后距离减少13%，垂直速度有类似幅度的降低将使飞行后距离减少25%。此外，运动员在推斥阶段施加的力对跳马的飞行后特征影响极小。针对离马的不同起跳距离，研究了优秀跳马所需的起跳速度。随着距离的减小，所需速度降低，但发现飞行前阶段身体所需的角速度会非常迅速地增加。
