运动员空中翻腾和转体姿态控制过程中转动惯量的变化

Changes of Moment of Inertia in Posture Control during Somersaults and Twists of Athletes

目的:分析运动员空中动作中转动惯量的变化特征。方法:根据跳水空中动作特点,建立人体多体系统模型,并开发相应的计算机仿真软件。对某运动员完成四个跳水动作(A:107B;B:407C;C:5136B;D:5235B)进行三维运动学分析和计算机仿真,获得人体总重心、外方位角及总转动惯量张量。最后计算对应于转体、翻腾和倾斜运动的三个中心主转动惯量I1、I2和I3。结果:总重心和外方位角的变化均符合真实运动情况。从四个动作的三个主转动惯量变化曲线看,I2和I3总比较接近,平均值约为I1的5倍。屈体或团身阶段时间约为0.2 s,而展开阶段约为0.1 s。动作A翻腾过程中I1变化较小,平均为2.12 kg·m2;翻腾阶段I2平均为3.46 kg·m2,翻腾结束时I2达最大,为12.48 kg·m2。动作B在翻腾过程中也是I1变化较小,平均为2.32 kg·m2;但I2在翻腾开始时最大,为13.62 kg·m2,翻腾阶段平均为3.30 kg·m2。动作C和D主转动惯量变化相似。动作C的转体阶段I1较小,平均为1.15 kg·m2,转体结束时可达到4.32 kg·m2;翻腾阶段I2最小,平均为3.65 kg·m2,结束时为12.95 kg·m2。结论:空中翻腾和转体过程中转动惯量呈快速、大范围变化,不同类型空中动作的惯性参量变化差异较大。本文建立了测量计算空中转动惯量变化的方法,为运动员分析空中姿态控制提供了新方法。

Objective In some sports events such as diving and gymnastics, athletes adjust moments of in- ertia by body and limb movements to control posture in aerial movements. This paper was to analyze the characteristics of moment of inertia in aerial movements. Methods A model of multibody system was found- ed based on features of aerial movements in diving, and corresponding computer simulation software was de- veloped. Four diving movements （A： 107B; B ： 407C; C ： 5136B; D： 5235B ） performed by an elite athlete were analyzed using 3D motion analysis method. Computer simulation of the four movements was per- formed, and center of mass, external orientation angles and inertia tensor of the human multi segment system over through the movements were obtained. Finally, the three central principle moments of inertia （I 1, I2, I3, corresponding to body movements of twist, somersaults and tilt） over through the movements were calculat- ed. Results The changes of center of mass and external orientation angles were all accord with the real move- ments. After observing the curves of the three central principle moments of inertia, it was found that I2 and I3 were always very close. Their average values were 5 times of that of I1. The phase of body pike or tuck du- ration was about 0.2 s, and that of extension was 0.1 s. There was less change and with an average of about 2.12 kg·m^2 in I1 during the somersault of A; the average of I2 was 3.46 kg·m^2 during the somersault, but I2 rose to maximum at the end of the somersault, 12.48 kg·m^2. As for B, there was less change and with an average of 2.32 kg·m^2 in I1; but I2 was at its maximum value, 13.62 kg·m^2 ,at the beginning of the somersault; the average of I2 during the somersault was 3.30 kg·m^2. The curves of central principle moments of inertia for C and D were close. During twist of C, I1 was low, 1.15 kg·m^2, and was 4.32 kg·m^2 at the end of the twist; I2 was at minimum value, 3.65 kg·m^2, but was 12.95 kg·m^2 at the end of somersault. Conclusion It is found that moments of inertia change rapidly in a large range during somersault and twist, and the curves of moments of inertia for different kinds of movement vary greatly. A method for measuring and calculating the moments of inertia has been developed in this paper, which would provide a new means for analyzing the posture control in aerial movement.