[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 demonstration Xueeng Wang Jilin nstitute o Physical Education, Changchun, Jilin, (CHNA) ABSTRACT With light simulation techniques application in military aircrat, table tennis theoretical model veriication also gradually starts to use light simulation techniques. The paper irstly states light simulation techniques concept, introduces light simulation system basic composition structure. Secondly, divide table tennis light into three phases that include racket and table tennis contacting process, table tennis air light process, table tennis and table collision process, and rom physics special knowledge perspective, targeted at every phase, it makes orce analysis. inally, analyze digital simulation, real object simulation and semi-real object simulation such three technical ways most suitable analytic table tennis theoretical model simulation technique rom analysis o speed, analysis o cost, and analysis o convenience and simulation eiciency our aspects. Research result shows, semi-real object simulation is the simulation technique that most suitable to analyze table tennis theoretical model. KEYWORDS Simulation technique; Table tennis; Theoretical model; Analytic hierarchy process; Mathematical model. Trade Science nc.
BTAJ, (3) 4 Xueeng Wang 6975 NTRODUCTON 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 Matlabsimulation technique, they veriied established model. 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 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. 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, experts 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. LGHT SMULATON TECHNQUE light simulation takes lying machine as research objects, establishes mathematical model according to kinematics, 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 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; its structure schematic graph is as igure shows. igure : Schematic diagram o the light simulator
6976 Table tennis light simulation techniques to theoretical model analytic demonstration BTAJ, (3) 4 rom igure, it is clear that control mechanism has bidirectional eects no matter or operators proprioception or lying machine sports equation set. THEORETCAL MODEL 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. 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. 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: direction is riction orce : mpact orce : = t t = dt dt And meanwhile, riction orce generates moment o orce Table tennis rotational inertia: D D, impulsive moment is c = mr, end speed that along direction is V, end speed that along 3 V, end angular speed is ω. On the basis o momentum theorem and angular momentum theorem, it can get: t dt. = mv = mv () () D = c ω (3) Decompose table tennis speed in horizontal direction v x and vertical direction v y, it can get table tennis out o racket instant speed (t is table tennis initial speed). v v = v sin θ + v cos θ = sin θ cos θ (4) m m x + y v sinθ v cosθ = sinθ cosθ m m = (5)
BTAJ, (3) 4 Xueeng Wang 6977 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 3 shows. igure 3 : The second phase o stress analysis diagram irstly regard table tennis moves in the two-dimensional plane xoy, rom igure 3, 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: G = mg (n general, g = 9.8m / s ) (6) buoyancy = ρgπ D 6 3 (7) d l C Av = d ρ ( d = C D 3 v Lρ γ ( L C is one table tennis resistance coeicient) (8) C is lit orce coeicient) (9) Make decomposition on igure 3 orces, it can get equation as ollowing: d x 3 m = C ρ sin θ + ρ L D v Cd Av dt d y 3 m = mg ρgπd dt 6 3 + C LρD γv cos θ + Cd ρav sin θ cos θ () Table tennis and table collision process n table tennis and table collision process, table tennis 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 4 shows. igure 4 : The third stage o stress analysis diagram
6978 Table tennis light simulation techniques to theoretical model analytic demonstration BTAJ, (3) 4 Assume speed that table tennis oblique collides the table is v e, rom igure 4, 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 and x u y, restitution coeicient is e, riction coeicient is μ. Analysis method and 3. 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: u x = vex + μvey ( e + ) u y = evey ' 3μ γ = γ v ( e + ) ey 4πr () When table tennis and table contact, its speed is opposite to assumed direction, it can get: u x = vex μvey ( e + ) u y = ev ey ' 3μ γ = γ + v ( e + ) ey 4πr () OPTMAL SMULATON TECHNQUE ON THEORETCAL MODEL ANALYSS 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 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. TABLE : mportance ranking Percentage (%) Ranking Simulation eiciency 5 Analysis o convenience 4.3 Analysis o speed 4. 3 Analysis o cost 9.4 4 AHP principles 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.
BTAJ, (3) 4 Xueeng Wang 6979 (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. Hierarchical structure is as igure 5. igure 5 : Hierarchical structure chart n igure 5, layer is target layer that is the purpose which is required to inally ulill or researching problems, layer is criterion layer that is the medium process that researching problems go through,layer 3 is scheme layer that is each kind o reerencing schemes. n general, the irst layer is one actor, the second and third layer has multiple actors and quantity is not ixed. 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, L, 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 x and x every time,uses a to express x and x to Z impacts ratios, all comparison is using matrix ( ) n n i j ij A = a ij to express, A has become judgment matrix between Z X. rom matrix, it is clear that i i Z impact ratio is a,then x and x to Z impact ratio is a a ij j i ji =. a According to linear algebra theoretical knowledge, i matrix ( ) n n = ( i, j =,, L n),then matrix A is positive reciprocal matrix. aij aij value determination can according to scale table, contents are as ollowing TABLE. ji, TABLE : Scale table ij i j a ij x and x to A = meets a > Scale Deinition ndicates two actors have equal importance by comparing 3 ndicates the ormer is slightly more important than the later by comparing two actors 5 ndicates the ormer is obviously more important than the later by comparing two actors 7 ndicates the ormer is intensely more important than the later by comparing two actors 9 ndicates the ormer is extremely more important than the later by comparing two actors, 4, 6, 8 ndicates middle level o above judgment Reciprocal importance ratio bet een i and j is a then importance ratio bet een j andi is a ij j and
698 Table tennis light simulation techniques to theoretical model analytic demonstration BTAJ, (3) 4 Result analysis n the model, target layer is optimal simulation technique, criterion layer is analysis o speed, analysis o cost, and analysis 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. TABLE 3 : Target layer paired comparison matrix A B B B 3 B 4 B 3 4 7 B /3 5 B /4 / 4 3 B /7 / /4 4 or judgment matrix concrete construction, it will not urther discuss. Use Matlab sotware program to solve, it can get result as TABLE 4. TABLE 4 : Result analysis Criterion Analysis o Analysis Analysis o Simulation speed o cost convenience eiciency Criterion layer weight.96.33.33.554 Semi-real object simulation Scheme layer single arrangement Real object simulation Digital simulation Total arrangement weight.4846.585.583.79.3943.355.637.47.78.355.646.48.637.649.354 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. CONCLUSON light simulation technique uses simulation theory, computer science and aeronautics and astronautics as well as others multiple disciplines theoretical knowledge. light simulation technique applies in sports research is an important sign o simulation technique urther development. The paper applies analytic hierarchy process in researching simulation types that it or table tennis theoretical model veriication, applies mathematical theories into practical research aspect, which shows in practical problems researches, select semi-real object simulation theory as veriying table tennis theoretical model s rationality to certain extent. REERENCES [] Liu Win-Ming, Tang Jian-jun; Study on the mixed strategy nash equilibrium in the game o "serve-serve reception" in table tennis competition[j], Journal o Beijing Sport University, 35(8), 34-38 (). [] Cao Li; Analysis o value added tax loss problem rom the angle o game comments[j], Journal o Pingyuan University, 4(3), -4 (7). [3] Ju Jiang; A research on the double service tactics used by excellent table tennis players[j], Liaoning Sport Science and Technology, 33(3), 85-87 (). [4] Dong Yang, Zhu eng, Jun, Gu Jian, Ping; Analysis on technique and tactics o the excellent oreign doubles in the 48th world table tennis championship[j], Journal o Chengdu Physical Education nstitute, 3(4), 73-75 (5). [5] (a) Shi Jian-Xin, Han Wen-xiu; Evolution o dynamic games and backward induction[j], Transactions o Tianjin University, 7(), (), (b) normation, 4, 3 (). [6] Yang Hua, Guan Zhi-Ming; Simulation o ping-pong trajectory based on ODE[J], Computer Simulation, 8(9), 3-33 (). [7] Sun Zai, Yu Guang-Xin, Guo Mei, Zhu Li-Li, Yang Jun, He Zheng-Bing; Aerodynamic principles o table tennis loop and numerical analysis o its lying route[j], China Sport Science, 8(4), 69-7 (8).
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