The simulation of table tennis during the course of sports / A simulação de tênis de mesa durante o curso de esportes. abstract.

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1 Boletim Técnico da Petrobras (Bulletin o Technology) - volume 6, p. 4-47, 7 SSN:6-67 SBN: Daoping Wang* Sports Department, Guangdong University o oreign Studies, Guangzhou 56, Guangdong, China @qq.com The simulation o table tennis during the course o sports / A simulação de tênis de mesa durante o curso de esportes KEYWORDS: Simulation technology, Analytic hierarchy process, Mathematical model abstract Simulation technology has been widely used in national deense construction, education, sports skills, and many other aspects. n the table tennis movement model, the simulation technique is applied to veriy the rationality o the model. This article irst expounds the concept o light simulation technology, this paper introduces the basic structure o light simulation system. Secondly, table tennis light can be divided into three stages, including the racket process o contact with the table tennis, table tennis in the process o air light, table tennis table and the process o collision, and rom the perspective o physical knowledge, to orce analysis or each stage. inally, rom the analysis speed, cost, ease o analysis and simulation results our aspects analysis and digital simulation, physical simulation, and the hardware-in-the-loop simulation o these three kinds o technology is most suitable or table tennis simulation technology o theory model. The results show that the semi-physical simulation is the most suitable or table tennis theory model simulation technology. PALAVRAS-CHAVE: Tecnologia de simulação, Processo de hierarquia analítica, Modelo matemático resumo A tecnologia de simulação tem sido amplamente utilizada na construção de deesa nacional, educação, habilidades esportivas e muitos outros aspectos. No modelo de movimento do tênis de mesa, a técnica de simulação é aplicada para veriicar a racionalidade do modelo. Este artigo expõe primeiro o conceito de tecnologia de simulação de vôo, este artigo apresenta a estrutura básica do sistema de simulação de vôo. Em segundo lugar, o voo de tênis de mesa pode ser dividido em três etapas, incluindo o processo de raquete de contato com o tênis de mesa, tênis de mesa no processo de vôo aéreo, mesa de tênis de mesa e o processo de colisão, e da perspectiva do conhecimento ísico, análise de orça para cada estágio. inalmente, a partir da análise de velocidade, custo, acilidade de análise e resultados de simulação, análise de quatro aspectos e simulação digital, simulação ísica e a simulação de hardware destes sistemas de três tipos são mais adequadas para a tecnologia de simulação de tênis de mesa de modelo teórico. Os resultados mostram que a simulação semi-ísica é a mais adequada para a tecnologia de simulação de modelos de tênis de mesa. 4

2 introduction The simulation o table tennis during the course o sports - Daoping Wang* section i With rapidly development o inormation technology, simulation technique gradually has more applications. Up to now, simulation technique has already been widely used in national deense construction, education research, sports technological research and so on multiple aspects. n table tennis sports model establishment, simulation technique is used to veriy model rationality. n 8, Jiang u-gao and others in the article Table tennis light kinematics model establishment and simulation, targeted at lying table tennis, they made orce analysis, analysis showed that table tennis during light process, except or suering gravity and air resistance inluences, it would also suer Magnus orce eects that caused by rotation. On this basis, authors established space coordinate system that was it or solving. Regarded Newton s second law as theoretical basis, they established mathematical model. By Matlab sotware, they made simulation processing with table tennis light trajectory, and then veriied model s rationality. n, Zhao Lei in the article Table tennis light process mechanical analysis and Matlab simulation, made analysis o the whole process that racket stroke ball and ball lied out o table ater colliding with table, established models rom mechanical perspective, and by Matlab simulation technique, they veriied established model. -5 n, Guo Hai-Jun in the article Table tennis robot dynamical analysis and joint simulation research, targeted at robot table tennis mechanical system and control system aspects, went deeper into theoretical analysis, and took real stroking environment as examples, made table tennis simulation analysis. or table tennis dynamical analysis, it mainly constructed dynamical equation through Lagrange method, according to light simulation techniques section ii light simulation takes lying machine as research objects, establishes mathematical model according to kinematics, ive orders polynomial, planned stroking trajectory, and utilized dynamical simulation to deine model rationality. According to table tennis movements, ball and racket as well as table collision, established stroking model, utilized predicted table tennis movement trajectory, planned stroking paths, and relected robot stroking scenes by simulation technique. With regard to robot control system, utilized speed, current and position tricyclic servomechanism theory, constructed control system s mathematical model, and deined systematic parameters by simulation techniques so as to implement systematic accurate controlling. 6-9 n, Zou Jun-Hua in the article Table tennis sports technology learning research in the view o inormation technology, highlighted that in inormation technological era, people should use inormation technology into practical teaching lie so as to promote education quality. Table tennis was Chinese national ball, but its sports techniques were not easy to grasp. Author research pointed out that in table tennis daily training, inormation technological application mainly contained curriculum management system, online learning environment, expert s animation examples and video eedback such our aspects. Curriculum management system generated certain impacts on table tennis trainers by techniques, social environment and attitudes and emotions as well as other actors. Online learning environment aected learners training initiative by situation, environment and other actors. n experts animation examples, they were implemented by decomposing motions, slow motions and playing rame by rame., The paper takes analytic hierarchy process as theoretical basis, makes comprehensive evaluation on light simulation techniques that are suitable to table tennis theoretical analysis rom multiple aspects. dynamics and light control theory as well as others multiple aspects proessional knowledge, and bases on the model to make experimental research. By ar, light simulation has been widely applied in aviation lying aspect; it provides essential help to lying machine development, production and utilization. According to simulation type and simulation implementation paths dierences, it can divide light simulation into digital simulation, real object 4

3 Boletim Técnico da Petrobras (Bulletin o Technology) - volume 6, p. 4-47, 7 SSN:6-67 SBN: simulation and semi-real object simulation three types. Digital simulation reers to utilize computer programs to implement pure digital calculation; it mainly is applied in lying machine perormance estimation and analysis. Real object simulation and semi-real object simulation mainly rely on computer, on the basis o adding peripheral equipment; create lying conditions that get closer to practice. light simulator includes air simulation and ground simulation, but narrow light simulator generally reers to group devices that can timely relect approximately real lying state in the ground. t is composed o computer, sound, vision and other systems; it is clear that control mechanism has bidirectional eects no matter or operators proprioception or lying machine sports equation set. section iii theoretical models or table tennis model, irstly it should go ahead with orce analysis, divide table tennis light into three phases, the irst phase is racket and table tennis contacting process, the second phase is table tennis air light process, and the third phase is table tennis and table collision process. 3. Racket contacts with table tennis Racket and table tennis contacting process suer two orces eects, one is racket to ball impact orce, second is racket and ball riction orce, in the process, it ignores gravity inluence, and regard both table tennis initial speed and initial angular speed as as igure shows. And meanwhile, riction orce generates moment o orce D D t, impulsive moment is dt. Table tennis rotational inertia: c = mr, end speed that 3 along direction is V, end speed that along direction is V, end angular speed is ω. On the basis o momentum theorem and angular momentum theorem, it can get ormula (-3): = mv () = mv () D = c ω Decompose table tennis speed in horizontal direction v x and vertical direction v y, it can get table tennis out o racket instant speed ormula (4) and ormula (5) (t is table tennis initial speed). vx = v sinθ + v cosθ = sinθ + cosθ (4) m m (3) v y = v sinθ v cosθ = sinθ cosθ (5) m m igure. The irst stage o stress analysis diagram n igure, it shows racket and table included angle isθ. Assume racket and table tennis contacting time is t, athlete swinging racket speed is v, table tennis mass is m, table tennis diameter is D. n the time rame o t, two orces impulses: riction orce : = t t dt mpact orce : = dt 3. Table tennis lying process Table tennis in lying process mainly suers three orces acting, one is sel-gravity, two is air buoyancy orce, and third is air resistance in alling process. n addition, table tennis in light process, it may occur to rotate, thereore it also should consider the existing o Magnus orce, and orce analysis schematic graph is as igure shows. 43

4 The simulation o table tennis during the course o sports - Daoping Wang* suered orces include two parts, one part is table to table tennis elastic orce, the other is table to table tennis riction orce, orce status is as igure 3 shows. igure : The second phase o stress analysis diagram irstly regard table tennis moves in the two-dimensional plane xoy, rom igure, it is clear that table tennis speed and horizontal included angle is θ, rotation speed is γ, when table tennis rotates, rotational axis is vertical to xoy. Gravity G, buoyancy orce buoyancy, resistance d and Magnus orce l solving process is as ollowing ormula (6-9): G = mg (n general, g = 9.8m / s ) (6) 3 buoyancy = ρgπd 6 (7) d = CdρAν (8) C D Make decomposition on igure 3 orces, it can get equation as ollowing ormula (): 3 = Lρ γν (9) d x 3 m = C sin cos LρD v θ + CdρAν θ dt d y 3 m = mg + ρgπd dt CLρD γν cosθ + CdρAν sinθ 3.3 Table tennis and table collision process () n table tennis and table collision process, table tennis section vi optimal simulation technique on theoretical model analysis igure 3: The third stage o stress analysis diagram Assume speed that table tennis oblique collides the table is v e, rom igure 3, it is clear that decompose it along horizontal direction and vertical direction, it can get v e x and v e y, speed that table tennis rebounds rom the table is u, decompose it along x and y direction into u x and u y, restitution coeicient is e, riction coeicient is µ. Analysis method and process method are basically the same. Result is as ollowing: When table tennis and table contact, its speed is consistent to assumed direction, it can get ormula (): ux = vex + µ vey ) uy = evey 3µ γ` = γ vey ) 4π r () When table tennis and table contact, its speed is opposite to assumed direction, it can get ormula (): ux = vex + µ vey ) uy = evey 3µ γ` = γ + vey ) 4π r () or table tennis theoretical model analysis light simulation technique, it includes digital simulation, real object simulation and semi-real object simulation three types. n practical analysis process, light simulation techniques selection is a relative complicate problem. The model establishment takes analytic hierarchy process as theoretical basis, and carries out rom 44

5 Boletim Técnico da Petrobras (Bulletin o Technology) - volume 6, p. 4-47, 7 SSN:6-67 SBN: analysis o speed, analysis o cost, and analysis o convenience and simulation eiciency our aspects. By lots o questionnaire survey, and process with investigation data, it can get the our aspects importance as Table shows. Percentage (%) Simulation eiciency 5 Analysis o convenience 4.3 Analysis o speed 4. 3 Analysis o cost AHP principles Table. mportance ranking Ranking AHP can solve relative tedious and vague problems decision-making problems. Use the method to construct model, it roughly needs our steps: Hierarchical structure establishment; Construct every layer that ully used in judgment matrix; Hierarchical single arrangement and consistency test; Hierarchical total arrangement and consistency test. n the ollowing, it respectively states each step detailed process. AHP solved problems are required to be hierarchic, orderly and logic. Only then it can construct hierarchical scheme. Let tedious problems elements to orm into multiple hierarchies according to its attributes, membership and its relations. Last hierarchical element plays a dominate role in next hierarchical relative elements. n general, these hierarchies can be divided into 3 types: () Top layer: Only one element in this hierarchy, it normally is inal target o analytic problems. The layer is also called target hierarchy. () Middle hierarchy: n this hierarchy, it includes intermediate links that get involved to ulill targets, which can be composed o some hierarchies that include multiple and multilayer criterions that required to consider. t can also be called criterion hierarchy. (3) The bottom hierarchy: This hierarchy includes optional each method and way to ulill targets. t can also be called measure hierarchy or scheme hierarchy. Hierarchy numbers in hierarchical structure have something to do with problem s complicated degree as well as analysis detailed requirements, normally the hierarchy numbers are not limited, each element in every hierarchy governs less than 9 elements. 4. Judgment matrix construction Each layer structure can show actors relationships, but in middle layer, each actor occupied proportion in target evaluation basically will not be ully the same, in the heart o evaluators, each actor has certain proportions. When deine each actor proportion that is to compare n pieces o actors X = { x,, x n } to actor Z impacts. Saaty and others proposed to carry out paired comparison among actors, and constructed comparison matrix method. That is to say, it selects two actors xi and x j every time, uses aij to express x and x to Z impacts ratios, all comparison is using i a ij matrix ( ) n n j A = to express, A has become judgment matrix between Z X.rom matrix, it is clear that i xi and x j to Z impact ratio is a ij,then x j and x i to Z impact ratio is a ji =. a According to linear algebra theoretical knowledge, i matrix A = ( a ij ) meets n n aij > and a ji = ( i, j =,,, n) a,then matrix A is positive reciprocal matrix. aij value determination can according to scale table; contents are as ollowing Table. Scale Deinition ndicates two actors have equal importance by comparing ndicates the ormer is slightly more important than the 3 later by comparing two actors ndicates the ormer is obviously more important than the 5 later by comparing two actors ndicates the ormer is intensely more important than the 7 later by comparing two actors ndicates the ormer is extremely more important than the 9 later by comparing two actors, 4, 6, 8 ndicates middle level o above judgment Reciprocal importance ratio between i and j is importance ratio between j and i is a Table. Scale table 4.3 Result analysis ij a ij,then ji =. aij n the model, target layer is optimal simulation technique, criterion layer is analysis o speed, analysis o cost, and analysis ij 45

6 The simulation o table tennis during the course o sports - Daoping Wang* o convenience and simulation eiciency; Scheme layer is digital simulation, real object simulation and semi-real object simulation. Target layer paired comparison matrix is as Table 3 shows. A B B B3 B4 B or judgment matrix concrete construction, it will not urther discuss. Use Matlab sotware program to solve, it can get result as Table 4. rom Table 4, it is clear that semi-real object simulation weight is the highest. t indicates that semi-real object simulation is most suitable to analyze and veriy table tennis theoretical model. B /3 5 B3 /4 / 4 B /7 / /4 4 Table 3. Target layer paired comparison matrix Criterion Analysis o speed Analysis o cost Analysis o convenience Simulation eiciency Criterion layer weight Scheme layer single arrangement Semi-real object simulation Real object simulation Digital simulation Table 4. Result analysis Total arrangement weight conclusion section v light simulation technology combined with simulation, computer science and learns the theory o multiple disciplines such as knowledge o aeronautics and astronautics. light simulation technology applied in the study o sports is the important symbol section vi reerences and notes [] G.H. Zhen, The Role o Endurance Contests in the Construction o Authority and Social Order in Rural China: Cases in the Qing Dynasty and the Republic o China. nt. J. Hist. Spor. 3(8), 57-7(5). or the urther development o simulation technology. n this paper, the analytic hierarchy process (ahp) is applied to research suitable or table tennis theory model validation o the simulation type, the mathematical theory is applied to the actual research aspect, rom a certain extent, illustrates the problems in the actual study, simulation study is chosen as the rationality o table tennis theory model is proved. [] B. Zhang, K.L. Qin, Q. Yang, Teaching Objectives and Teaching Content Point o View the Concept o Sports Teaching and the Comparison o the Chinese Sports Teaching. nt. J. Huma. Soci. Scie. Edu. 3(6), 4-45(6). [3] W.J. Jiang, K.L. Qin, B. Huang,. Li, Huanggang Middle School Basketball Teaching Present Situation and Countermeasure Research. nt. J. Huma. Soci. Scie. Edu. 3(6), 5-57(6). 46

7 Boletim Técnico da Petrobras (Bulletin o Technology) - volume 6, p. 4-47, 7 SSN:6-67 SBN: [4] L. Liu, Quantitative study and analysis or English integrated teaching based on Matlab. J. Chem. Pharm. Res. 6(5), (4). [5] H. Jiang, 4, Chinese mens basketball team development countermeasure research based on analytic hierarchy process. J. Chem. Pharm. Res. 6(5), (4). [6]. Li, X.X. Jia, G. Du, E. A. Ghaar, The analysis o actors aecting the development o tennis based on principal component analysis. Biotechnol. An ndian J. 8(6), (3). [7] W.Z. Song, Study on the analysis and simulation o osbury lop technique based on the sports biomechanics. Biotechnol. An ndian J. 8(), (3). [8] C. Chen, G. Lu, E. A. Ghaar, Mathematical model o nonlinear distortion and linear error correction or soccer robot vision system. Biotechnol. An ndian J. 8(6), (3). [9] S. Pu, Biomechanical analysis o the inluencing actors on itness running leg s stomp eect. n. Technol. J. (9), (3). [] B. Zhang, X.. Cao, W.J. Jiang, L. Liu,. Li, Grey clustering analysis-based tennis racket o nanometer materials kinematic mechanics applied research. J. Comput. Theor. Nanosci. (), 38-3(5). [] D.y. Tang, G. Ma, J. Guo, Applications o Monte Carlo algorithm in research on the basketball hit rate o ideal hollow shooting based on Matlab Simulation. n. Technol. J. (5), (3). 47

An Indian Journal FULL PAPER ABSTRACT KEYWORDS. Trade Science Inc.

An Indian Journal FULL PAPER ABSTRACT KEYWORDS. Trade Science Inc. [Type text] [Type text] [Type text] SSN : 974-7435 Volume ssue 3 BioTechnology 4 An ndian Journal ULL PAPER BTAJ, (3), 4 [6974-698] Table tennis light simulation techniques to theoretical model analytic