CN110327611A - A kind of platform diving evaluation method that athletic type's coefficient is added - Google Patents

A kind of platform diving evaluation method that athletic type's coefficient is added Download PDF

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CN110327611A
CN110327611A CN201910520234.1A CN201910520234A CN110327611A CN 110327611 A CN110327611 A CN 110327611A CN 201910520234 A CN201910520234 A CN 201910520234A CN 110327611 A CN110327611 A CN 110327611A
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athlete
diving
time
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颜成钢
郑锦凯
朱晨
孙垚棋
张继勇
张勇东
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Hangzhou Dianzi University
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Abstract

本发明公开了一种加入运动员体型系数的跳台跳水评价方法。本发明将跳水运动员简化为一个带有旋转运动的刚体,通过研究刚体运动的时间与刚体的质量、长度的关系来描述运动员的跳水时间和运动员体重、身高的关系,具体实现步骤如下:步骤1、将运动员的跳水动作简化为五个阶段;步骤2、基于跳水运动员的身高和体重进行运动员完成跳水动作时间的建模;步骤3:基于步骤2中得出的模型建立跳水运动员新的难度系数评价体系,具体的根据跳水运动员完成跳水动作时间和运动员身高体重的数学模型建立跳水运动员新的难度系数评价体系。本发明能够很好的得出运动员体型系数。

The invention discloses a platform diving evaluation method adding athletes' body shape coefficients. The present invention simplifies the diving athlete into a rigid body with rotational motion, and describes the relationship between the diving time of the athlete and the weight and height of the athlete by studying the relationship between the time of the rigid body motion and the quality and length of the rigid body. The specific implementation steps are as follows: Step 1 1. Simplify the diving action of the athlete into five stages; step 2, model the time for the athlete to complete the diving action based on the height and weight of the diver; step 3: establish a new difficulty factor for the diving athlete based on the model obtained in step 2 The evaluation system is to establish a new difficulty coefficient evaluation system for diving athletes based on the mathematical model of the diving athlete's time to complete the diving action and the athlete's height and weight. The present invention can obtain the athlete's body shape coefficient very well.

Description

一种加入运动员体型系数的跳台跳水评价方法An Evaluation Method of Platform Diving Adding Athlete's Body Size Coefficient

技术领域technical field

本发明涉及刚体动力学领域,具体的说,是将跳水运动员体型系数加入进去的旋转刚体运动,并以此给出更加公平的跳台跳水评价方法The present invention relates to the field of rigid body dynamics, specifically, it is a rotating rigid body motion that adds the body shape coefficient of divers into it, and provides a more fair evaluation method for platform diving

背景技术Background technique

我国跳水队曾在上世纪90年代开始领先世界各国,中国跳水队在多次世界性大赛中取得了举世瞩目的辉煌成绩,也被国人称为“梦之队”。但随着世界跳水运动中动作难度的不断提升,且创新不断,造成中国跳水队在动作难度上已无明显优势。特别是男子10米台项目中,从2004年希腊雅典奥运会之后到2012年伦敦奥运会,我国再也没有登上男子10米台的最高领奖台。纵观当今跳水强国,无不是在以动作表现稳、准、美的基础上,不断向动作难度方面进行突破与创新。而难度加大之后,对运动员的身高、体重等方面会有更加严格的标准,因目前国际泳联十米跳台跳水难度系数的确定规则并未设置体型校正系数,所以目前这种难度系数评价方法在公平性方面有所缺失。The Chinese diving team started to lead the world in the 1990s. The Chinese diving team has achieved brilliant results that have attracted worldwide attention in many world competitions, and is also called the "dream team" by the Chinese. However, with the continuous improvement of the difficulty of movements in world diving and continuous innovation, the Chinese diving team has no obvious advantage in the difficulty of movements. Especially in the men's 10-meter platform event, from the 2004 Athens Olympics in Greece to the 2012 London Olympics, my country has never reached the highest podium in the men's 10-meter platform. Looking at today's diving powerhouses, all of them are constantly making breakthroughs and innovations in terms of movement difficulty on the basis of stable, accurate and beautiful movements. After the difficulty increases, there will be stricter standards for the height and weight of the athletes. Because the current FINA rules for determining the difficulty coefficient of the 10-meter platform diving do not set a body shape correction coefficient, the current evaluation method for the difficulty coefficient There is a lack of fairness.

发明内容Contents of the invention

本发明主要考虑跳水运动员在跳台跳水项目中完成各个跳水动作与运动员体型(身高、体重)之间的关系。从而得出体型矫正系数,进而给出加入体型矫正系数后的新的难度系数评分体系。The present invention mainly considers the relationship between divers completing each diving action in the platform diving event and the athlete's body shape (height, weight). Thus, the body shape correction coefficient is obtained, and then a new difficulty coefficient scoring system after adding the body shape correction coefficient is given.

本文将跳水运动员简化为一个带有旋转运动的刚体(注:下文中提到的刚体即为跳水运动员),从而可以通过研究刚体运动的时间与刚体的质量、长度的关系来描述运动员的跳水时间和运动员体重、身高的关系。In this paper, the diver is simplified as a rigid body with rotational motion (note: the rigid body mentioned below is the diver), so that the diving time of the athlete can be described by studying the relationship between the time of the rigid body movement and the quality and length of the rigid body Relationship with athlete's weight and height.

步骤1、将运动员的跳水动作简化为五个阶段;Step 1, simplify the diving action of the athlete into five stages;

所述的五个阶段分别为:The five stages described are:

第一阶段:纯翻腾运动;The first stage: pure somersault movement;

第二阶段:手臂张开;The second stage: arms open;

第三阶段:带有转体和翻腾的刚体运动;The third stage: rigid body motion with rotation and somersault;

第四阶段:手臂收拢,类似阶段二,但手臂沿相反方向运动;Phase 4: Arms folded in, similar to Phase 2, but the arms move in the opposite direction;

第五阶段:手臂收拢后的纯翻腾的刚体运动。The fifth stage: the pure tumbling rigid body motion after the arms are closed.

尽管我们在这里对跳水运动员的跳水动作做了极大的简化处理,只考虑了运动员的翻腾、转体和手臂张开或关闭这三种动作,但是这种简化是合理的。因为倘若将所有跳水动作,诸如抱膝、屈体、倒立等等一系列动作都考虑在内,无异于给模型增加建模难度,很可能直接导致模型无法建立,而现在这种简化既能保留跳水项目中比较典型的几个跳水动作,又能帮助我们建立模型分析讨论出跳水运动时间与运动员身高、体重之间的关系。接下来我们简单介绍刚体运动中的一些基本规律。Although we have greatly simplified the diver's diving action here, only considering the three movements of the athlete's somersault, twist, and arm opening or closing, this simplification is reasonable. Because if all diving movements, such as knee tuck, knee bend, handstand, etc., are taken into account, it is tantamount to adding difficulty to the model, which may directly lead to the failure of the model to be established, and now this simplification can both Retaining several typical diving movements in diving events can help us establish a model to analyze and discuss the relationship between diving time and athlete's height and weight. Next, we briefly introduce some basic laws of rigid body motion.

步骤2、基于跳水运动员的身高和体重进行运动员完成跳水动作时间的建模;Step 2, based on the height and weight of the diver, the modeling of the time for the athlete to complete the diving action is carried out;

我们用Ι表示空间固定框架中的常角动量矢量,并在该固定框架中建立一个直角坐标系,由于在模型假设中,忽略了空气阻力的影响,故刚体运动过程中角动量守恒,该坐标系的原点可以建立在任意位置。同时,用L表示参考系中随体运动(人体运动)的角动量矢量,并以人的质心为原心建立空间坐标系。用R表示从一个框架(坐标系)到另一个框架(坐标系)的旋转矩阵。用Ω表示3维空间中的角速度。用A表示形状改变导致的动量偏移;用A表示形状改变导致的动量偏移;We use Ι to represent the constant angular momentum vector in a fixed space frame, and establish a rectangular coordinate system in the fixed frame. Since the influence of air resistance is ignored in the model assumption, the angular momentum is conserved during the motion of the rigid body. The coordinate The origin of the system can be established at any position. At the same time, L is used to represent the angular momentum vector of body motion (human body motion) in the reference frame, and a space coordinate system is established with the center of mass of the person as the original center. Let R represent the rotation matrix from one frame (coordinate system) to another. Use Ω to represent the angular velocity in 3-dimensional space. Let A represent the momentum shift caused by the shape change; use A to represent the momentum shift caused by the shape change;

相关文献提出I=RL,并进而证明得到以及Ω=I-1(L-A)。随后通过以上公式推导得出带有旋转运动的刚体满足以下运动方程:Relevant literature proposes I=RL, and then proves that and Ω=I −1 (LA). Then it is derived from the above formula that the rigid body with rotational motion satisfies the following equation of motion:

其中,l是空间固定框架中的常角动量矢量,φ表示物体的翻转角,θ表示倾斜角,表示扭转角,h表示手臂张开或关闭引起的内部角动量且于时间无关,h=wd·Ιd,I1、I2、I3分别为物体在X轴、Y轴、Z轴上的转动惯量;Among them, l is the constant angular momentum vector in the space fixed frame, φ represents the flip angle of the object, θ represents the tilt angle, Represents the torsion angle, h represents the internal angular momentum caused by the opening or closing of the arm and has nothing to do with time, h=w d · Ι d , I 1 , I 2 , and I 3 are the objects on the X-axis, Y-axis, and Z-axis respectively moment of inertia;

因为张开手臂是一瞬间的事情,所用的时间相对于刚体运动的总时间来说很小,所以我们这里不妨假设张开手臂转过180度的完成时间为0.25秒,进而得到手臂张开引起的角速度ωd=4πrad/s,Ιd表示张开手臂引起的内部转动惯量,这里我们同样简化处理为Ιd=2kg·m2,得到手臂张开引起的内部角动量h=8πN·m·s。根据角动量守恒原理,刚体在整个运动过程中,角动量始终不变,我们常理分析结合角动量公式,即假设一个体重为50kg的女运动员,她的旋转半径为0.7m,角速度同上取值为4πrad/s,则l=mr2ω=50·0.72·4π=307.7N·m·s,我们这里对刚体整体的角动量进行合理取值l=300N·m·s。Because opening the arm is an instant thing, the time used is relatively small compared to the total time of rigid body motion, so we might as well assume that the completion time of opening the arm to turn 180 degrees is 0.25 seconds, and then get the arm opening. The angular velocity ω d = 4πrad/s, Ι d represents the internal moment of inertia caused by opening the arm, here we also simplify the treatment as Ι d = 2kg m 2 , and obtain the internal angular momentum h = 8πN · m caused by the opening of the arm s. According to the principle of conservation of angular momentum, the angular momentum of a rigid body remains unchanged during the entire movement process. We analyze the common sense and combine the angular momentum formula, that is, suppose a female athlete with a weight of 50kg has a radius of rotation of 0.7m, and the angular velocity is the same as above. 4πrad/s, then l=mr 2 ω=50·0.7 2 ·4π=307.7N·m·s, here we take a reasonable value l=300N·m·s for the overall angular momentum of the rigid body.

公式(1)中的分别表示φ,θ,对无量纲时间的导数,且有如下关系式:In the formula (1) Respectively represent φ, θ, for dimensionless time The derivative of , and has the following relationship:

其中 in

这里我们假设五个阶段中所有的动作都是对称的情况,在对称的情况下,有的关系,所以运动方程(2)可化简为:Here we assume that all the actions in the five stages are symmetrical. In the symmetrical case, there are relationship, so the motion equation (2) can be simplified as:

其中 in

下面我们按照之前提到的五个阶段对公式(3)进行讨论。Below we discuss formula (3) according to the five stages mentioned above.

首先,设T1,T2,T3,T4,T5分别为完成五个阶段的动作所用的时间,对应的无量纲时间分别为 First, let T 1 , T 2 , T 3 , T 4 , and T 5 be the time taken to complete the five stages of action respectively, and the corresponding dimensionless time is

阶段一:纯翻腾运动Phase 1: Pure somersault movement

在纯翻腾动作中,有且没有因手臂张开或者关闭而引起的内部角动量,即h=0,从而有进而得到原函数 In pure somersault action, there is And there is no internal angular momentum caused by the opening or closing of the arm, that is, h=0, so there is and then get the original function

阶段二:手臂张开Phase Two: Arms Open

该运动过程中,我们可以得到θ有了一个微小的变化,为方便讨论,我们在该阶段中统一取值θ=θmax,相关文献提出During this movement, we can get There is a slight change in θ. For the convenience of discussion, we uniformly take the value θ=θ max at this stage. Related literature proposes

这是第一类完全椭圆积分,通过令z=sinθ,并取值γ=19,我们可以求出上述定积分的表达式为This is the first kind of complete elliptic integral. By setting z=sinθ and taking the value γ=19, we can obtain the expression of the above definite integral as

其中k函数是由P.F.Byrd等人提出一种计算公式。in The k function is a calculation formula proposed by PFByrd et al.

不难发现,关于公式(5)十分复杂,但考虑到实际问题中,手臂张开只是一瞬间的动作,该时间相对于刚体运动的总时间微乎其微,为了方便我们建模分析,此处我们再次对近似处理为0,并忽略手臂张开对身体其他部位的影响,即身体倾斜度θ不变,仍为0。It is not difficult to find that the formula (5) is very complicated, but considering the actual problem, the opening of the arm is only a momentary movement, and this time is very small compared to the total time of the rigid body movement. In order to facilitate our modeling and analysis, here we again right The approximate processing is 0, and the influence of the arm opening on other parts of the body is ignored, that is, the body inclination θ remains unchanged and is still 0.

阶段三:手臂张开后的翻腾的刚体运动Phase 3: Tumbling rigid body motion after the arm is opened

基于上述阶段二中的简化处理,可以得出θ仍为0,仍为并且此时刚体处于纯翻腾的平衡运动,同样没有因手臂张开或者关闭而引起的内部角动量,即h=0,从而有ρ=0,得到原函数 Based on the simplified processing in the second stage above, it can be concluded that θ is still 0, still for And at this time, the rigid body is in a pure tumbling balance motion, and there is no internal angular momentum caused by the opening or closing of the arms, that is, h=0, so ρ=0, get the original function

阶段四:手臂闭合Phase Four: Arm Closure

该阶段与阶段二类似,有 This stage is similar to stage two, with

阶段五:手臂闭合后的纯翻腾运动Phase 5: Pure somersault movement after arm closure

此阶段类似阶段一,有 This stage is similar to stage 1, with

分析到这里,我们可以得出刚体运动的总时间为From the analysis here, we can conclude that the total time of rigid body motion is

which is

我们发现这里的转动惯量I是一个关于质量m的函数,在三维空间中,有如下关系:We find that the moment of inertia I here is a function of mass m, and in three-dimensional space, there is the following relationship:

其中x,y,z分别表示刚体在三轴方向上离旋转中心的距离。Among them, x, y, and z represent the distance of the rigid body from the center of rotation in the three-axis direction, respectively.

基于实际情况分析可知,上述三个距离均为定值,我们同样对其分别合理取值为x=y=0.5,式(7)变形为Based on the analysis of the actual situation, it can be seen that the above three distances are all fixed values, and we also reasonably set the values of x=y=0.5, Equation (7) is transformed into

将公式(8),h=0,l=300带入式(1)得:Put formula (8), h=0, l=300 into formula (1) to get:

注:因为阶段一和阶段三中,手臂均无张开或闭合运动,所以这两阶段中因手臂摆动而引起的内部角动量h均为0。Note: Because there is no opening or closing movement of the arm in stage 1 and stage 3, the internal angular momentum h caused by arm swing in these two stages is 0.

可由式(9)得出:It can be obtained from formula (9):

可得出原函数 The original function can be obtained

又因为φ1=2πn1,φ3=2πn3,其中n1,n3分别为阶段一和阶段三中翻腾的周数,从而可以得出:And because φ 1 = 2πn 1 , φ 3 = 2πn 3 , where n 1 and n 3 are the number of tossing cycles in stage 1 and stage 3 respectively, so it can be drawn:

其中n=n1+n3where n=n 1 +n 3 .

下面对上述所建模型进行验证:The above model is verified as follows:

我们以郭晶晶为例来验证模型的合理性。通过查阅资料我们可以得知郭晶晶的身高1.63米,体重48公斤,假设她的跳水动作是翻转两圈,也就是将m=48,h=1.63,n=2带入到公式(12)中有:We take Guo Jingjing as an example to verify the rationality of the model. By consulting the data, we can know that Guo Jingjing is 1.63 meters tall and weighs 48 kilograms. Assume that her diving action is to flip twice, that is, put m=48, h=1.63, and n=2 into the formula (12). :

与实际情况相符,从而可以验证我们模型的合理性。 It is consistent with the actual situation, so that the rationality of our model can be verified.

从定性角度思考,通过式(12)可知,质量越大,跳水动作时间越长。这一点与生活中体型越大的物体惯性越大,他们的行动速度相对缓慢的常识相吻合,从而进一步证明了我们所建模型的合理性。Thinking from a qualitative point of view, it can be seen from formula (12) that the greater the mass, the longer the diving action time. This is consistent with the common sense that the larger the objects in life, the greater the inertia, and their moving speed is relatively slow, which further proves the rationality of our model.

步骤3:基于步骤2中得出的模型建立跳水运动员新的难度系数评价体系,具体的根据跳水运动员完成跳水动作时间和运动员身高体重的数学模型建立跳水运动员新的难度系数评价体系,并得出运动员体型矫正系数,具体实现如下:Step 3: Establish a new difficulty coefficient evaluation system for divers based on the model obtained in step 2. Specifically, establish a new difficulty coefficient evaluation system for divers based on the mathematical model of the diver's time to complete the diving action and the athlete's height and weight, and obtain The athlete's body shape correction coefficient is specifically implemented as follows:

同一个动作,相同的难度系数,不同的运动员去完成却需要不同的时间,这都是因为个人的身高体重等个人身体因素所造成的,且时间Ttot的三维图像随着运动员身高体重的变化而变化,这就体现出,完成时间Ttot对于每个运动员都有着特异性,即每个运动员都有着自己所对应的完成时间,设图3中运动员所完成的跳水动作的难度系数为D,将D放入图3中,得到图4。The same action, the same degree of difficulty, different athletes need different time to complete it, which is caused by personal physical factors such as personal height and weight, and the three-dimensional image of time T tot changes with the height and weight of athletes And change, this just shows that the completion time T tot has specificity for each athlete, that is, each athlete has its own corresponding completion time, assuming that the difficulty coefficient of the diving action completed by the athlete in Figure 3 is D, Putting D into Figure 3 yields Figure 4.

图中平面即为该跳水动作的难度系数D,在这里声明,此难度系数D与坐标轴中运动员身高/m、运动员体重/kg没有直接的函数关系。The plane in the figure is the difficulty coefficient D of the diving action. It is stated here that the difficulty coefficient D has no direct functional relationship with the athlete's height/m and athlete's weight/kg in the coordinate axis.

由于完成动作的时间Ttot与运动员身高体重有着明显的函数关系,且能够反映不同运动员的特异性,所以如果将图4中时间T曲面的弯曲程度应用到难度系数D曲面上,则难度系数D曲面也就能够根据不同的运动员的身体参数反映出不同的难度系数;Since the time T tot to complete the action has an obvious functional relationship with the athlete's height and weight, and can reflect the specificity of different athletes, if the curvature of the time T surface in Figure 4 is applied to the difficulty coefficient D surface, then the difficulty coefficient D The curved surface can also reflect different difficulty coefficients according to the physical parameters of different athletes;

此种思想简单来说就是在原有难度系数的基础上,将由于身高体重变化导致的时间曲面T弯曲程度的变化映射到难度系数曲面D上,使之能够反映不同运动员做同一动作所对应的难度系数。所采取的方法是将时间曲面T的值直接加到难度系数D曲面上,从而得到新的难度系数曲面,后来发现这样得到难度系数较大,也不严谨,所以在时间曲面T取一合适的中心点值t0,得到如下表达式:Simply put, this idea is to map the change in the curvature of the time surface T due to height and weight changes to the difficulty coefficient surface D on the basis of the original difficulty coefficient, so that it can reflect the difficulty corresponding to different athletes doing the same action coefficient. The method adopted is to directly add the value of the time surface T to the surface of the difficulty coefficient D to obtain a new difficulty coefficient Surface, it was later found that the difficulty coefficient of obtaining in this way is relatively large, and it is not rigorous, so take a suitable center point value t0 on the time surface T, and get the following expression:

式中Ttot为问题二所建模型计算得出的实际时间,t0为上文时间T曲面中间点,D为旧的难度系数曲面,为新的难度系数曲面,为校正系数。In the formula, T tot is the actual time calculated by the model built in question 2, t0 is the middle point of the above time T surface, D is the old difficulty coefficient surface, is the new difficulty coefficient surface, is the correction coefficient.

本发明有益效果如下:The beneficial effects of the present invention are as follows:

本发明将跳水运动员简化为一个带有旋转运动的刚体(注:下文中提到的刚体即为跳水运动员),从而可以通过研究刚体运动的时间与刚体的质量、长度的关系来描述运动员的跳水时间和运动员体重、身高的关系。The present invention simplifies the diver into a rigid body with rotational motion (note: the rigid body mentioned hereinafter is the diver), so that the diving of the athlete can be described by studying the relationship between the time of the rigid body motion and the quality and length of the rigid body The relationship between time and athlete's weight and height.

本发明通过建立模型反映运动员完成各个跳水动作的时间与运动员体型(身高,体重)之间的关系,得出体型矫正系数,进而给出加入运动员体型系数后的新的难度系数评价方法。The invention builds a model to reflect the relationship between the time for athletes to complete each diving action and the athlete's body shape (height, weight), obtains the body shape correction coefficient, and then provides a new difficulty coefficient evaluation method after adding the athlete's body shape coefficient.

在讨论跳水运动的时间与运动员体型之间的函数关系时,对一些不必要的参数,做了合理的简化处理,在保证模型的正确性的基础上,提高了建模的可行性,该简化思想可应用在其他建模问题中。When discussing the functional relationship between the diving time and the athlete's body shape, some unnecessary parameters were reasonably simplified, and the feasibility of the modeling was improved on the basis of ensuring the correctness of the model. The simplification Ideas can be applied to other modeling problems.

另外,本发明所建模型在定性,定量两方面均得到了正确的验证,表明所建模型是合理的,比较符合实际情况的,具有一定的实用性,对提高评价跳水运动员评分的公平性有一定的参考意义。In addition, the model built by the present invention has been correctly verified both qualitatively and quantitatively, showing that the model built is reasonable, more in line with actual conditions, has certain practicability, and has a certain effect on improving the fairness of evaluating diving athletes. Certain reference significance.

附图说明Description of drawings

图1是以人的质心为原心建立的空间坐标系图;Figure 1 is a diagram of a space coordinate system established with the center of mass of a person as the original center;

图2是存在倾斜角θ与扭转角的空间坐标系图;Figure 2 shows the existence of inclination angle θ and twist angle The spatial coordinate system diagram of ;

图3是不同身高体重的运动员完成同一动作所需的时间曲面图;Fig. 3 is the time surface graph that athletes of different heights and weights complete the same action;

图4是加入难度系数曲面作为对比的时间曲面图;Figure 4 is a time surface diagram with the difficulty coefficient surface added as a comparison;

图5是将T曲面的弯曲程度应用于D曲面的时间曲线图;Fig. 5 is a time curve diagram of applying the bending degree of the T curved surface to the D curved surface;

具体实施方式Detailed ways

基于前面所得出的结论:人的身高体重与运动员完成各个跳水动作时间之间有函数关系,因此可以通过收集大量跳水运动员的身高体重数据,使用前面所得出的模型,算出他们在完成同一个跳水动作时不同的大致完成时间,并将之绘成三维图形时间T曲面,如图3所示:Based on the previous conclusions: there is a functional relationship between the height and weight of a person and the time it takes for athletes to complete each diving action. Therefore, by collecting a large number of data on the height and weight of divers and using the model obtained earlier, it can be calculated that they are completing the same diving action. Different approximate completion times of actions, and draw it into a three-dimensional graphic time T surface, as shown in Figure 3:

由图可知,在完成同一跳水动作时,体重越大、身高越高的运动员较体重较轻、身高稍矮的远动员所要花费的时间更久,同样,完成的难度也就相对较大;但在实际的比赛中,不同的运动员完成同一个动作所获得的难度系数得分却是相同的,这是极不公平的,身材瘦小的灵活运动员在身材方面占了很大的便宜,所以在跳台跳水运动中,是很有必要设置体型矫正参数的,以求实现比赛的公平。It can be seen from the figure that when completing the same diving movement, the heavier and taller athlete takes longer than the lighter weight and shorter athlete. Similarly, the difficulty of completion is relatively greater; but In actual competitions, different athletes get the same difficulty score for the same action, which is extremely unfair. Small and flexible athletes take a big advantage in terms of body size, so when diving on the platform In sports, it is necessary to set body shape correction parameters in order to achieve fairness in the game.

同一个动作,相同的难度系数,不同的运动员去完成却需要不同的时间,这都是因为个人的身高体重等个人身体因素所造成的,且时间Ttot的三维图像随着运动员身高体重的变化而变化,这就体现出,完成时间Ttot对于每个运动员都有着特异性,即每个运动员都有着自己所对应的完成时间,设图3中运动员所完成的跳水动作的难度系数为D,将D放入图3中,得到图4。The same action, the same degree of difficulty, different athletes need different time to complete it, which is caused by personal physical factors such as personal height and weight, and the three-dimensional image of time T tot changes with the height and weight of athletes And change, this just shows that the completion time T tot has specificity for each athlete, that is, each athlete has its own corresponding completion time, assuming that the difficulty coefficient of the diving action completed by the athlete in Figure 3 is D, Putting D into Figure 3 yields Figure 4.

图中平面即为该跳水动作的难度系数D,在这里声明,此难度系数D与坐标轴中运动员身高/m、运动员体重/kg没有直接的函数关系。The plane in the figure is the difficulty coefficient D of the diving action. It is stated here that the difficulty coefficient D has no direct functional relationship with the athlete's height/m and athlete's weight/kg in the coordinate axis.

由于完成动作的时间Ttot与运动员身高体重有着明显的函数关系,且能够反映不同运动员的特异性,所以如果将图4中时间T曲面的弯曲程度应用到难度系数D曲面上,则难度系数D曲面也就能够根据不同的运动员的身体参数反映出不同的难度系数,具体的应用方法效果图如图5所示。Since the time T tot to complete the action has an obvious functional relationship with the athlete's height and weight, and can reflect the specificity of different athletes, if the curvature of the time T surface in Figure 4 is applied to the difficulty coefficient D surface, then the difficulty coefficient D The curved surface can also reflect different difficulty coefficients according to the physical parameters of different athletes. The specific application method effect diagram is shown in Figure 5.

此种思想简单来说就是在原有难度系数的基础上,将由于身高体重变化导致的时间曲面T弯曲程度的变化映射到难度系数曲面D上,使之能够反映不同运动员做同一动作所对应的难度系数。所采取的方法是将时间曲面T的值直接加到难度系数D曲面上,从而得到新的难度系数曲面,后来发现这样得到难度系数较大,也不严谨,所以在时间曲面T取一合适的中心点值t0,此时t0所对应的m=50kg,h=1.6米,n为翻腾周数,n=3,可求出t0=1.24秒,所在,得到如下表达式:Simply put, this idea is to map the change in the curvature of the time surface T due to height and weight changes to the difficulty coefficient surface D on the basis of the original difficulty coefficient, so that it can reflect the difficulty corresponding to different athletes doing the same action coefficient. The method adopted is to directly add the value of the time surface T to the surface of the difficulty coefficient D to obtain a new difficulty coefficient Curved surface, it was later found that the degree of difficulty obtained in this way is relatively large and not rigorous, so take a suitable center point value t0 on the time surface T, and at this time t0 corresponds to m=50kg, h=1.6 meters, n is the number of tumbling cycles, n=3, can obtain t0=1.24 second, where, obtain following expression:

式中Ttot为问题二所建模型计算得出的实际时间,t0为上文时间T曲面中间点,D为旧的难度系数曲面,为新的难度系数曲面,为校正系数。In the formula, T tot is the actual time calculated by the model built in question 2, t0 is the middle point of the above time T surface, D is the old difficulty coefficient surface, is the new difficulty coefficient surface, is the correction coefficient.

实施例Example

我们以郭晶晶的身高1.63m,体重48kg为例,带入上面的模型中,求出新的等式其中n为翻腾周数(翻腾圈数的一半)。计算结果如下表所示,明显我们的结果与表1中原有的难度系数有较大差别。Let's take Guo Jingjing's height of 1.63m and weight of 48kg as an example, bring it into the above model, and find a new equation Among them, n is the number of tumbling cycles (half of the number of tumbling circles). The calculation results are shown in the table below. It is obvious that our results are quite different from the original difficulty coefficients in Table 1.

造成有差别的原因正如上面的解答一致,The reason for the difference is consistent with the above answer,

表1:十米跳台难度系数表(部分动作)Table 1: Ten-meter platform difficulty coefficient table (partial movements)

[动作代码说明](1)第一位数表示起跳前运动员起跳前正面朝向以及翻腾方向,1、3表示面朝水池,2、4表示背向水池;1、2表示向外翻腾,3、4表示向内翻腾。(2)第三位数字表示翻腾圈数,例如407,表示背向水池,向内翻腾3周半。(3)B表示屈体,C表示抱膝。(4)如果第一位数字是5,表示有转体动作,此时,第二位数字意义同说明(1),第三位数字表示翻腾圈数,第四位数字表示转体圈数,例如5375,表示面向水池向内翻腾3周半,转体2周半。[Description of action codes] (1) The first digit indicates the frontal orientation of the athlete before take-off and the direction of somersault, 1, 3 means facing the pool, 2, 4 means facing away from the pool; 1, 2 means somersault outwards, 3, 4 means toss inwards. (2) The third digit indicates the number of tumbling circles, for example, 407, which means turning the back to the pool and tossing inward for 3 and a half weeks. (3) B means flexion, and C means tuck. (4) If the first digit is 5, it means that there is a turning movement. At this time, the meaning of the second digit is the same as that in the explanation (1), the third digit indicates the number of tumbling circles, and the fourth digit indicates the number of turning circles. For example, 5375 means toss inward facing the pool for 3 and a half weeks, and turn for 2 and a half weeks.

Claims (4)

1.一种加入运动员体型系数的跳台跳水评价方法,其特征在于将跳水运动员简化为一个带有旋转运动的刚体,通过研究刚体运动的时间与刚体的质量、长度的关系来描述运动员的跳水时间和运动员体重、身高的关系,具体实现步骤如下:1. A platform diving evaluation method that adds athlete's body shape coefficient, is characterized in that diving athlete is simplified as a rigid body with rotary motion, describes the diving time of athlete by the time of research rigid body motion and the quality of rigid body, the relation of length The relationship between weight and height of athletes, the specific implementation steps are as follows: 步骤1、将运动员的跳水动作简化为五个阶段;Step 1, simplify the diving action of the athlete into five stages; 所述的五个阶段分别为:The five stages described are: 第一阶段:纯翻腾运动;The first stage: pure somersault movement; 第二阶段:手臂张开;The second stage: arms open; 第三阶段:手臂张开后,带有转体和翻腾的刚体运动;The third stage: After the arms are opened, rigid body motion with rotation and somersault; 第四阶段:手臂收拢,类似阶段二,但手臂沿相反方向运动;Phase 4: Arms folded in, similar to Phase 2, but the arms move in the opposite direction; 第五阶段:手臂收拢后的纯翻腾的刚体运动;The fifth stage: pure tumbling rigid body motion after the arms are closed; 步骤2、基于跳水运动员的身高和体重进行运动员完成跳水动作时间的建模;Step 2, based on the height and weight of the diver, the modeling of the time for the athlete to complete the diving action is carried out; 步骤3:基于步骤2中得出的模型建立跳水运动员新的难度系数评价体系,具体的根据跳水运动员完成跳水动作时间和运动员身高体重的数学模型建立跳水运动员新的难度系数评价体系。Step 3: Establish a new difficulty coefficient evaluation system for divers based on the model obtained in step 2. Specifically, establish a new difficulty coefficient evaluation system for divers based on the mathematical model of the diver's time to complete the diving action and the athlete's height and weight. 步骤4、根据难度系数评价体系,得出运动员体型矫正系数。Step 4. According to the difficulty coefficient evaluation system, the athlete's body shape correction coefficient is obtained. 2.根据权利要求1所述的一种加入运动员体型系数的跳台跳水评价方法,其特征在于步骤2所述的建模具体实现如下:2. a kind of platform diving evaluation method that adds sportsman's body shape coefficient according to claim 1, it is characterized in that the modeling concrete realization described in step 2 is as follows: 用Ι表示空间固定框架中的常角动量矢量,并在该固定框架中建立一个直角坐标系,由于在模型假设中忽略空气阻力影响,故刚体运动过程中角动量守恒,该坐标系的原点可建立在任意位置;同时,用L表示参考系中随体运动的角动量矢量,并以人的质心为原心建立空间坐标系;用R表示从一个框架到另一个框架的旋转矩阵;用Ω表示3维空间中的角速度;用A表示形状改变导致的动量偏移;Use Ι to represent the constant angular momentum vector in the fixed frame of space, and establish a rectangular coordinate system in the fixed frame. Since the influence of air resistance is ignored in the model assumption, the angular momentum is conserved during the motion of the rigid body, and the origin of the coordinate system can be It is established at any position; at the same time, use L to represent the angular momentum vector of body motion in the reference system, and establish a space coordinate system with the center of mass of the person as the original center; use R to represent the rotation matrix from one frame to another frame; use Ω Represents the angular velocity in 3-dimensional space; A represents the momentum shift caused by the shape change; 由于I=RL,得到以及Ω=I-1(L-A);随后通过以上公式推导得出带有旋转运动的刚体满足以下运动方程:Since I=RL, we get And Ω=I -1 (LA); then the rigid body with rotational motion satisfies the following equation of motion by deriving the above formula: 其中,l是空间固定框架中的常角动量矢量,φ表示物体的翻转角,θ表示倾斜角,表示扭转角,h表示手臂张开或关闭引起的内部角动量且于时间无关,h=wd·Ιd,I1、I2、I3分别为物体在X轴、Y轴、Z轴上的转动惯量;Among them, l is the constant angular momentum vector in the space fixed frame, φ represents the flip angle of the object, θ represents the tilt angle, Represents the torsion angle, h represents the internal angular momentum caused by the opening or closing of the arm and has nothing to do with time, h=w d · Ι d , I 1 , I 2 , and I 3 are the objects on the X-axis, Y-axis, and Z-axis respectively moment of inertia; 假设张开手臂转过180度的完成时间为0.25秒,进而得到手臂张开引起的角速度ωd=4π rad/s,Ιd表示张开手臂引起的内部转动惯量,简化处理为Ιd=2kg·m2,得到手臂张开引起的内部角动量h=8πN·m·s;根据角动量守恒原理,设一个体重为m1的女运动员,她的旋转半径为r1,角速度同上取值为ω1,则角动量l=m1r12ω1;Assuming that the completion time of opening the arm to turn 180 degrees is 0.25 seconds, and then obtaining the angular velocity ω d =4π rad/s caused by the opening of the arm, Ι d represents the internal moment of inertia caused by opening the arm, and the simplified process is Ι d = 2kg ·m 2 , get the internal angular momentum h=8πN·m·s caused by the opening of the arm; according to the principle of conservation of angular momentum, suppose a female athlete whose weight is m1, her rotation radius is r1, and the angular velocity is ω1 as above. Then the angular momentum l=m1r1 2 ω1; 公式(1)中的分别表示φ,θ,对无量纲时间的导数,且有如下关系式:In the formula (1) Respectively represent φ, θ, for dimensionless time The derivative of , and has the following relationship: 其中, in, 设五个阶段中所有动作均对称,则有的关系,所以运动方程(2)可化简为:Assuming that all actions in the five stages are symmetrical, then relationship, so the motion equation (2) can be simplified as: 其中, in, 根据五个阶段对公式(3)进行讨论,设T1,T2,T3,T4,T5分别为完成五个阶段的动作所用的时间,对应的无量纲时间分别为 Discuss formula (3) according to the five stages, let T 1 , T 2 , T 3 , T 4 , T 5 be the time taken to complete the actions of the five stages respectively, and the corresponding dimensionless times are 3.根据权利要求2所述的一种加入运动员体型系数的跳台跳水评价方法,其特征在于步骤3所述的新的难度系数评价体系,具体实现如下:3. a kind of platform diving evaluation method that adds sportsman body shape coefficient according to claim 2, is characterized in that the new degree of difficulty evaluation system described in step 3, concrete realization is as follows: 第一阶段:纯翻腾运动Phase 1: Pure somersault movement 且没有因手臂张开或者关闭而引起的内部角动量,即h=0,从而有ρ=0,进而得到原函数 Have And there is no internal angular momentum caused by the opening or closing of the arm, that is, h=0, so ρ=0, and then get the original function 第二阶段:手臂张开Phase Two: Arms Open θ有变化,在该阶段中统一取值θ=θmax,则:Have θ has a change, and the value θ=θ max is uniformly taken at this stage, then: 这是第一类完全椭圆积分,通过令z=sinθ,并取值γ=19,能够求出上述定积分的表达式为:This is the first kind of complete elliptic integral. By setting z=sinθ and taking the value γ=19, the expression of the above definite integral can be obtained as follows: 其中k函数是由P.F.Byrd等人提出一种计算公式;in The k function is a calculation formula proposed by PFByrd et al.; 考虑到实际问题中,对近似处理为0,并忽略手臂张开对身体其他部位的影响,即身体倾斜度θ不变,仍为0;Considering the practical problems, the The approximate processing is 0, and the influence of the arm opening on other parts of the body is ignored, that is, the body inclination θ remains unchanged and is still 0; 第三阶段:手臂张开后,带有转体和翻腾的刚体运动;The third stage: After the arms are opened, rigid body motion with rotation and somersault; 有θ为0,由于此时刚体处于纯翻腾的平衡运动,没有因手臂张开或者关闭而引起的内部角动量,即h=0,从而有ρ=0,得到原函数 have θ be 0, for Since the rigid body is in a pure tumbling equilibrium motion at this time, there is no internal angular momentum caused by the opening or closing of the arm, that is, h=0, so ρ=0, get the original function 第四阶段:手臂收拢,类似阶段二,但手臂沿相反方向运动;Phase 4: Arms folded in, similar to Phase 2, but the arms move in the opposite direction; 该阶段与阶段二类似,有 This stage is similar to stage two, with 第五阶段:手臂收拢后的纯翻腾的刚体运动;The fifth stage: pure tumbling rigid body motion after the arms are closed; 此阶段类似阶段一,有 This stage is similar to stage 1, with 从而得出刚体运动的总时间为Thus, the total time of the rigid body motion is which is 由于转动惯量I是一个关于质量m的函数,在三维空间中,有如下关系:Since the moment of inertia I is a function of mass m, in three-dimensional space, there is the following relationship: 其中x,y,z分别表示刚体在三轴方向上离旋转中心的距离;Among them, x, y, and z respectively represent the distance of the rigid body from the center of rotation in the three-axis direction; 基于实际情况分析可知,上述三个距离均为定值,对其分别合理取值为x=y=0.5,式(7)变形为Based on the analysis of the actual situation, it can be seen that the above three distances are all fixed values, and their reasonable values are respectively x=y=0.5, Equation (7) is transformed into 将公式(8),h=0,l=300带入式(1)得:Put formula (8), h=0, l=300 into formula (1) to get: 由于第一阶段和第三阶段中,手臂均无张开或闭合运动,所以这两阶段中因手臂摆动而引起的内部角动量h均为0;Since there is no opening or closing movement of the arm in the first stage and the third stage, the internal angular momentum h caused by the swing of the arm in these two stages is 0; 可由式(9)得出:It can be obtained from formula (9): 可得出原函数 The original function can be obtained 又因为φ1=2πn1,φ3=2πn3,其中n1,n3分别为第一阶段和第三阶段中翻腾的周数,从而得出:And because φ 1 = 2πn 1 , φ 3 = 2πn 3 , where n 1 and n 3 are respectively the number of tossing cycles in the first stage and the third stage, thus: 其中,n=n1+n3Among them, n=n 1 +n 3 . 4.根据权利要求3所述的一种加入运动员体型系数的跳台跳水评价方法,其特征在于步骤4所述的运动员体型矫正系数,具体求解如下:4. a kind of platform diving evaluation method adding athlete's body shape coefficient according to claim 3, is characterized in that the athlete's body shape correction coefficient described in step 4, concrete solution is as follows: 将时间曲面T的值直接加到跳水动作的难度系数曲面D上,从而得到新的难度系数曲面,并在时间曲面T取中心点值t0,得到如下表达式:Add the value of the time surface T directly to the difficulty coefficient surface D of the diving action to obtain a new difficulty coefficient surface, and take the center point value t0 on the time surface T, the following expression is obtained: 式中Ttot为问题二所建模型计算得出的实际时间,t0为上文时间T曲面中间点,D为旧的难度系数曲面,为新的难度系数曲面,为校正系数。In the formula, T tot is the actual time calculated by the model built in question 2, t0 is the middle point of the above time T surface, D is the old difficulty coefficient surface, is the new difficulty coefficient surface, is the correction coefficient.
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