CN110327611A

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

Info

Publication number: CN110327611A
Application number: CN201910520234.1A
Authority: CN
Inventors: 颜成钢; 郑锦凯; 朱晨; 孙垚棋; 张继勇; 张勇东
Original assignee: Hangzhou Dianzi University
Current assignee: Hangzhou Dianzi University
Priority date: 2019-06-17
Filing date: 2019-06-17
Publication date: 2019-10-15

Abstract

The invention discloses a kind of platform diving evaluation methods that athletic type's coefficient is added.Diver is reduced to the rigid body for having rotary motion by the present invention, diving time and the sportsman's weight, the relationship of height of sportsman are described by studying the time of rigid motion and the quality of rigid body, the relationship of length, the specific implementation steps are as follows: the dive of sportsman is reduced to five stages by step 1；Step 2, the height based on diver and weight carry out the modeling that sportsman completes the dive time；Step 3: based on the new degree-of-difficulty factor appraisement system of the model foundation diver obtained in step 2, the new degree-of-difficulty factor appraisement system of diver specifically being established according to the mathematical model that diver completes dive time and sportsman's height and weight.The present invention can be good at obtaining athletic type's coefficient.

Description

Diving platform diving evaluation method added with body form coefficient of athlete

Technical Field

The invention relates to the field of rigid body dynamics, in particular to a rotating rigid body motion with the addition of the body form coefficient of a diving athlete, and provides a fairer diving platform diving evaluation method

Background

China's diving team has been leading the world in the last 90 th century, and the Chinese diving team has seen a remarkable brilliant result in many world races, and is also called "dream team" by the Chinese. However, with the continuous improvement of the action difficulty in the world diving sports and continuous innovation, the Chinese diving team has no obvious advantage in the action difficulty. Particularly, in 10-meter project for men, from the 10-meter project of Athens Olympic Games in Greenwich, 2004 to the Olympic Games in London, 2012, China has no top prize-receiving station for men, which is 10 meters. Through the current strong diving country, no breakthrough or innovation is continuously made to the action difficulty aspect on the basis of stable, accurate and beautiful action performance. After the difficulty is increased, stricter standards are provided for the height, the weight and the like of the athlete, and the current difficulty coefficient evaluation method is lacked in the fairness aspect because the body type correction coefficient is not set in the determination rule of the current international swimming union ten-meter diving tower diving difficulty coefficient.

Disclosure of Invention

The invention mainly considers the relation between each diving action and the body type (height and weight) of the diving athlete finished by the diving athlete in the diving project of the diving platform. Thereby obtaining the body shape correction coefficient and further providing a new difficulty coefficient scoring system after the body shape correction coefficient is added.

The diving athlete is simplified into a rigid body with rotary motion (note: the rigid body is referred to as the diving athlete hereinafter), so that the relation between the diving time of the athlete and the weight and the height of the athlete can be described by researching the relation between the time of the rigid body motion and the mass and the length of the rigid body.

Step 1, simplifying diving actions of athletes into five stages;

the five stages are respectively as follows:

the first stage is as follows: pure churning movement;

and a second stage: the arms are opened;

and a third stage: rigid body motion with swivel and billowing;

a fourth stage: the arm is folded, similar to the second stage, but the arm moves along the opposite direction;

the fifth stage: the arm is folded to perform pure tumbling rigid body movement.

Although we have made a great simplification of the diving action of a diving athlete here, considering only three actions of the athlete's billowing, turning, and arm opening or closing, this simplification is reasonable. If all diving actions, such as holding knees, bending bodies, standing upside down and the like, are taken into consideration, the modeling difficulty is not increased for the model, and the model is likely to be directly incapable of being established. We will next briefly introduce some basic rules in rigid body motion.

Step 2, modeling the time of the diving athlete to finish diving action based on the height and the weight of the diving athlete;

an I is used for representing a constant angular momentum vector in a space fixed frame, a rectangular coordinate system is established in the fixed frame, and because the influence of air resistance is neglected in the model assumption, the angular momentum is conserved in the rigid motion process, and the origin of the coordinate system can be established at any position. Meanwhile, the angular momentum vector of the satellite motion (human body motion) in the reference system is represented by L, and a space coordinate system is established by taking the center of mass of a human as the origin. The rotation matrix from one frame (coordinate system) to the other frame (coordinate system) is denoted by R. The angular velocity in 3-dimensional space is denoted by Ω. The momentum shift caused by the shape change is denoted by a; the momentum shift caused by the shape change is denoted by a;

the relevant literature proposes that I is equal to RL and further proves thatAnd Ω ═ I^-1(L-A). The rigid body with rotational motion is then derived by the above formula to satisfy the following equation of motion:

where l is the constant angular momentum vector in the spatially-stationary frame, [ phi ] denotes the flip angle of the object, [ theta ] denotes the tilt angle,representing the torsion angle, h representing the internal angular momentum due to arm opening or closing and independent of time, h ═ w_d·Ι_d，I₁、I₂、I₃The moment of inertia of the object on the X axis, the Y axis and the Z axis respectively;

because the arm is opened in a moment, the time is very small relative to the total time of rigid body motion, so we do not assume that the completion time of 180 degrees of arm opening rotation is 0.25 seconds, and then obtain the angular velocity omega caused by arm opening_d＝4πrad/s，Ι_dShowing the internal moment of inertia caused by opening the arm, here we also simplify the process to I_d＝2kg·m²The internal angular momentum h due to the arm opening is obtained as 8 pi N · m · s. According to the principle of angular momentum conservation, the angular momentum of a rigid body is constant in the whole movement process, and the formula of the angular momentum is combined through the routine analysis, namely, if a female player with the weight of 50kg is assumed, the rotating radius of the female player is 0.7m, the angular speed is 4 pi rad/s as above, and l equals to mr²ω＝50·0.7²We here make a reasonable value for the angular momentum of the whole rigid body, i.e. 300N · m · s.

In formula (1)Respectively, indicate the values of phi, theta,for dimensionless timeAnd has the following relationship:

wherein

Here we assume that all the actions in the five phases are symmetrical, in which case there areSo equation of motion (2) can be simplified as:

wherein

In the following we discuss equation (3) in terms of the five stages mentioned earlier.

First, let T₁,T₂,T₃,T₄,T₅Respectively, the time taken for completing the five phases of actions, and the corresponding dimensionless time respectively

Stage one: pure churning sports

In pure billowing action, there areAnd there is no internal angular momentum due to the arms opening or closing, i.e. h is 0, and thus there isFurther obtain the primitive function

And a second stage: arm opening

During the movement, we can obtainTheta has a slight variation, and for the sake of convenience of discussion, we take the value theta ═ theta uniformly at this stage_maxThe related documents propose

This is a first type of complete elliptic integral, and by making z sin θ and γ 19, we can find the above-mentioned definite integral as expressed in

WhereinThe k function is a calculation formula proposed by p.f. byrd et al.

It can be easily found that the equation (5) is quite complex, but considering the practical problem that the arm opening is only a moment, the time is very little relative to the total time of the rigid motion, and for the convenience of modeling analysis, we can make a pair of motions againThe approximation is 0 and the influence of the arm opening on other parts of the body is ignored, i.e. the body inclination theta is not changed and is still 0.

And a third stage: rigid body movement of turning over after arms are opened

Based on the simplified processing in stage two above,it can be derived that theta is still 0,is still asAnd the rigid body is in the pure tumbling equilibrium motion, and the internal angular momentum caused by the opening or closing of the arm is not existed, i.e. h is 0, so that p is 0,get primitive functions

And a fourth stage: arm closure

The stage is similar to the stage two in that

And a fifth stage: pure tumbling movement after arm closing

This stage is similar to stage one, having

Analysis to this point, we can derive the total time of rigid body motion as

Namely, it is

We find that the moment of inertia I here is a function of mass m, in three dimensions, in the following relationship:

where x, y, z respectively represent distances of the rigid body from the rotation center in the three-axis directions.

Based on the analysis of practical situation, the three distances are all constant values, and we also reasonably take the values of x, y and 0.5 respectively,the formula (7) is modified into

By referring to the formula (8),h is 0, l is 300, and the formula (1) is obtained:

note: since the arms do not have opening or closing motions in the first and third stages, the internal angular momentum h caused by the swinging of the arms in the two stages is 0.

This can be derived from equation (9):

the primitive functions can be obtained

And due to phi₁＝2πn₁，φ₃＝2πn₃Wherein n is₁，n₃The number of turns in stage one and stage three, respectively, can be derived as follows:

wherein n is n₁+n₃。

The above-created model was verified as follows:

we take Guo Jing as an example to verify the rationality of the model. By looking up the data, we can know that the height of guo crystal is 1.63m and the weight is 48kg, and suppose that the diving action of her is to turn over two circles, i.e. m is 48, h is 1.63, and n is 2, which is introduced into the formula (12):

the method is consistent with the actual situation, so that the reasonability of the model can be verified.

From a qualitative point of view, it is understood from the equation (12) that the larger the mass, the longer the diving action time. This is consistent with the knowledge that the larger the body shape, the larger the inertia of the object, the slower the moving speed of the object, and further proves the rationality of the model built by us.

And step 3: establishing a new difficulty coefficient evaluation system of the diving athlete based on the model obtained in the step 2, specifically establishing the new difficulty coefficient evaluation system of the diving athlete according to the diving action time of the diving athlete and the mathematical model of the height and the weight of the athlete, and obtaining the body shape correction coefficient of the athlete, and specifically realizing the following steps:

the same action, the same difficulty coefficient, different athletes need different time to finish, all caused by personal physical factors such as height, weight and the like of the individual, and the time T_totThe three-dimensional image of (A) changes along with the change of the height and the weight of the athlete, which shows that the completion time T_totEach athlete has specificity, that is, each athlete has the corresponding completion time, the difficulty coefficient of the diving action completed by the athlete in fig. 3 is set as D, and D is put into fig. 3 to obtain fig. 4.

The plane in the figure is the difficulty coefficient D of the diving action, and the difficulty coefficient D is stated to have no direct functional relation with the height/m and the weight/kg of the athlete in the coordinate axis.

Due to the time T of completing the action_totThe curve degree of the time T curve in the graph 4 is applied to the difficulty coefficient D curve, so that the difficulty coefficient D curve can reflect different difficulty coefficients according to body parameters of different athletes;

the idea is simply that on the basis of the original difficulty coefficient, the change of the bending degree of the time curved surface T caused by the change of the height and the weight is mapped to the difficulty coefficient curved surface D, so that the difficulty coefficients corresponding to the same action of different athletes can be reflected. The adopted method is to directly add the value of the time curved surface T to the difficulty coefficient D curved surface, thereby obtaining a new difficulty coefficientThe surface, which was later found to have a greater difficulty factor and is not strict, takes a suitable center point value T0 at time T to obtain the following expression:

in the formula T_totThe actual time calculated for the model created for problem two, T0 is the middle point of the surface at time T above, D is the old difficulty coefficient surface,for a new difficulty coefficient surface,is a correction factor.

The invention has the following beneficial effects:

the invention simplifies the diving athlete into a rigid body with rotary motion (note: the rigid body is the diving athlete hereinafter), thereby describing the relation between the diving time of the athlete and the weight and height of the athlete by researching the relation between the time of the rigid body motion and the mass and length of the rigid body.

According to the invention, the relationship between the time of finishing each diving action of the athlete and the body type (height and weight) of the athlete is reflected by establishing the model, so that the body type correction coefficient is obtained, and further, a new difficulty coefficient evaluation method after the body type coefficient of the athlete is added is provided.

When the functional relation between the diving time and the body type of the athlete is discussed, some unnecessary parameters are reasonably simplified, the feasibility of modeling is improved on the basis of ensuring the correctness of the model, and the simplifying idea can be applied to other modeling problems.

In addition, the model established by the invention is correctly verified in both qualitative and quantitative aspects, which shows that the established model is reasonable, relatively accords with the actual situation, has certain practicability and has certain reference significance for improving the fairness of evaluating the scores of the diving athletes.

Drawings

FIG. 1 is a diagram of a spatial coordinate system established with a centroid of a person as an origin;

FIG. 2 shows the existence of the inclination angle θ and the torsion angleA spatial coordinate system diagram of (a);

FIG. 3 is a graph of the time required for athletes of different heights and weights to complete the same activity;

FIG. 4 is a graph of a time surface with difficulty coefficient surfaces added for comparison;

FIG. 5 is a time plot of the degree of curvature of a T surface applied to a D surface;

Detailed Description

Based on the conclusions drawn above: the height and weight of the person have a functional relationship with the time of each diving action completed by the athlete, so that the height and weight data of a large number of diving athletes can be collected, the obtained model is used for calculating different approximate completion times of the athletes completing the same diving action, and the approximate completion times are drawn into a three-dimensional graph time T curved surface, as shown in figure 3:

as can be seen from the figure, when the same diving action is completed, the athlete with larger weight and higher height spends longer time than the athlete with lighter weight and shorter height, and the difficulty of completion is relatively larger; however, in the actual game, the difficulty coefficient scores obtained by different athletes completing the same action are the same, which is extremely unfair, and flexible athletes with thin and small figures account for very large cheapness in terms of figures, so that in the diving sports of the diving platform, it is necessary to set body shape correction parameters to realize the fairness of the game.

Due to the time T of completing the action_totThe time T curve in the figure 4 is applied to the difficulty coefficient D curve, so that the difficulty coefficient D curve can reflect different difficulty coefficients according to body parameters of different athletes, and a specific application method effect diagram is shown in figure 5.

The idea is simply that on the basis of the original difficulty coefficient, the change of the bending degree of the time curved surface T caused by the change of the height and the weight is mapped to the difficulty coefficient curved surface D, so that the difficulty coefficients corresponding to the same action of different athletes can be reflected. The adopted method is to curve the time surfaceThe value of T is directly added to the D surface of the difficulty coefficient, thereby obtaining a new difficulty coefficientSince the curved surface is found to have a large difficulty coefficient and is not strict, a suitable center point value T0 is taken for the curved surface T at a time, where m is 50kg, h is 1.6 m, n is the number of churns, n is 3, and T0 is 1.24 seconds, and the following expression is obtained:

Examples

We take Guo Jing crystal with height of 1.63m and weight of 48kg as an example, and introduce the above model to find out a new equationWhere n is the number of turnover cycles (half of the number of turnover cycles). The calculation results are shown in the following table, and it is obvious that our results are greatly different from the original difficulty coefficients in table 1.

The reason for the difference is as the above solution is consistent,

TABLE 1 Ten meters diving tower difficulty coefficient table (partial action)

[ motion code description ] (1) the first digit indicates the player's frontal orientation and tumble direction before take-off, 1, 3 indicates the frontal orientation towards the pool, and 2, 4 indicates the dorsal orientation towards the pool; 1.2 indicates eversion and 3, 4 indicates eversion. (2) The third digit indicates the number of turns, e.g. 407, and indicates turning back to the sink and turning in for 3 and a half weeks. (3) B represents flexion, and C represents holding the knee. (4) If the first digit is 5, it indicates that there is turning action, at this time, the second digit has the same meaning as description (1), the third digit indicates the number of turns, and the fourth digit indicates the number of turns, for example 5375, which indicates 3 turns and 2 turns facing the pool.

Claims

1. A diving platform diving evaluation method added with body type coefficients of athletes is characterized in that a diving athlete is simplified into a rigid body with rotary motion, and the relation between diving time of the athlete and the weight and height of the athlete is described by researching the relation between the time of the rigid body motion and the quality and length of the rigid body, and the method is concretely implemented by the following steps:

step 1, simplifying diving actions of athletes into five stages;

the five stages are respectively as follows:

the first stage is as follows: pure churning movement;

and a second stage: the arms are opened;

and a third stage: after the arms are opened, the rigid body with the turning body and the turning body moves;

the fifth stage: the pure tumbling rigid body movement after the arms are folded;

and step 3: and (3) establishing a new difficulty coefficient evaluation system of the diving athlete based on the model obtained in the step (2), and specifically establishing the new difficulty coefficient evaluation system of the diving athlete according to the diving action time of the diving athlete and the mathematical model of the height and the weight of the athlete.

And 4, obtaining the body shape correction coefficient of the athlete according to the difficulty coefficient evaluation system.

2. The diving evaluation method of claim 1, wherein the modeling of step 2 is implemented as follows:

i represents a constant angular momentum vector in a space fixed frame, a rectangular coordinate system is established in the fixed frame, and the angular momentum is conserved in the rigid body motion process because the air resistance influence is neglected in the model hypothesis, and the origin of the coordinate system can be established at any position; meanwhile, expressing the angular momentum vector of the satellite motion in the reference system by L, and establishing a space coordinate system by taking the center of mass of a person as an origin; denote by R the rotation matrix from one frame to the other; the angular velocity in 3-dimensional space is represented by Ω; the momentum shift caused by the shape change is denoted by a;

since I is RL, obtainAnd Ω ═ I^-1(L-A); the rigid body with rotational motion is then derived by the above formula to satisfy the following equation of motion:

assuming that the completion time of 180-degree rotation of the opened arm is 0.25 second, the angular velocity omega caused by the opened arm is obtained_d＝4π rad/s，Ι_dRepresents the internal moment of inertia caused by opening the arm, and is simplified by I_d＝2kg·m²To obtain the arm openingInternal angular momentum h due to opening is 8 pi N · m · s; according to the principle of angular momentum conservation, if a female player with the weight of m1 is provided, her rotation radius is r1, the angular velocity is the same as omega 1, and the angular momentum l is m1r1²ω1；

wherein,

if all the actions in the five stages are symmetrical, then there areSo equation of motion (2) can be simplified as:

wherein,

discussing equation (3) in terms of five stages, let T₁,T₂,T₃,T₄,T₅Respectively, the time taken for completing the five phases of actions, and the corresponding dimensionless time respectively

3. The diving evaluation method added with athlete body form factor of diving tower according to claim 2, characterized in that the new difficulty factor evaluation system of step 3 is implemented as follows:

the first stage is as follows: pure churning sports

Is provided withAnd there is no internal angular momentum due to the arm opening or closing, i.e., h is 0, so that ρ is 0,further obtain the primitive function

And a second stage: arm opening

Is provided withThere is a change in theta, the value theta being unity at this stage_maxAnd then:

this is a first type of complete elliptic integral, and by making z sin θ and γ 19, the expression for the above-mentioned fixed integral can be found as follows:

whereinThe k function is a calculation formula proposed by p.f. byrd et al;

in consideration of practical problems, theThe approximation processing is 0, and the influence of the opening of the arm on other parts of the body is ignored, namely the body inclination theta is not changed and is still 0;

there is a value of theta which is 0,is composed ofBecause the rigid body is in the pure tumbling equilibrium motion, there is no internal angular momentum caused by the opening or closing of the arm, i.e. h is 0, so that ρ is 0,get primitive functions

the stage is similar to the stage two in that

this stage is similar to stage one, having

Thereby obtaining the total time of the rigid body motion as

Namely, it is

Since the moment of inertia I is a function of mass m, in three-dimensional space, the following relationship holds:

wherein x, y and z respectively represent the distance from the rotation center of the rigid body in the three-axis direction;

based on the analysis of practical situation, the three distances are all constant values, and the values of x and y are 0.5,the formula (7) is modified into

in the first stage and the third stage, the arms do not have opening or closing motion, so that the internal angular momentum h caused by the swinging of the arms in the two stages is 0;

this can be derived from equation (9):

the primitive functions can be obtained

And due to phi₁＝2πn₁，φ₃＝2πn₃Wherein n is₁，n₃The number of weeks billed in the first and third stages, respectively, to yield:

wherein n is n₁+n₃。

4. The diving evaluation method of claim 3, wherein the athlete body shape correction factor of step 4 is specifically solved as follows:

the value of the time curved surface T is directly added to the difficulty coefficient curved surface D of the diving action, so that a new difficulty coefficient is obtainedAnd taking the central point value T0 of the surface T at the time to obtain the following expression: