Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations

With the continuous development of the economy, people's living standards are steadily improving, and the demand for education is increasing, tennis is popular as a fashionable and recreational activity. However, the traditional teaching mode is inefficient and lacks systematization and completeness, which affects the effectiveness of classroom teaching and causes a series of problems. In order to solve these problems, this paper designs a tennis mobile support system in the mode of teaching assistance, which aims to improve the efficiency of the classroom and increase the interest of students. The software uses web-based technology and web platform for database management and data interaction. In the development process, the main control module, control functions and other related variables are written in B/S programming language[1]. At the same time, we use Java language to build the model to realize the functions, and finally combine each sub-entity into a complete application, and compare and summarize the effect of classroom learning with the traditional teaching mode[2].

In foreign countries, in the early 1970s, multimedia classrooms were introduced in physical education in some universities. This not only provides convenience for students but also brings a lot of convenience for school management and publicity and education. With the rapid spread of information technology such as Internet technology and computer network communication technology and the expansion of application fields, these network technologies have transformed and upgraded the traditional classroom model[3]. More and more colleges and universities are considering this new form of multimedia classroom when building their own teaching platform, and assistive teaching is also one of the very important research areas. Based on the design of mobile multimedia classroom, the basic information, video and user registration functions of the tennis auxiliary system are implemented to provide students with a convenient way to learn[4,5].

With the development of the Internet, mobile video teaching is also gradually emerging. One of the common denominators is the use of web technology. The design of tennis assistance systems through the Internet is mainly through the database to achieve the exchange of information, data and other interactive functions, and it can analyze and organize these contents, so as to come up with solutions for users to use as a reference basis to achieve better results[6]. Another significant feature is that the software can provide services anytime and anywhere in real time and sharing, which creates possible conditions for users to communicate with each other and learn through the software, thus improving the utilization of information and facilitating the tennis sports assistance system[7,8]. Therefore, this paper is based on the design of some common problems in mobile video-assisted teaching.

javaSwing technology: it is a new technology popular in recent years, its main function is to provide some query and browsing services, through this system can realize a lot of course information, video materials and other related content. The use of this technology in tennis teaching can better help students improve their learning efficiency. javaSwing technology structure is shown in Figure 1.

Figure 1

solidworks development tools: solidworks is a general-purpose software, which can help users to provide a lot of practical, convenient and powerful tools, it is very convenient to use. This paper focuses on a solidworks-based tennis assistance system, which uses Myeclipse as the development tool and a variety of modular methods to achieve simple functional operation of each sub-module.

B/S structure: B/S structure is a database technology-based, process-oriented and object engineering system, whose structure is shown in Figure 2. It has two main types: one is to process the data directly, and the other is to analyze the data interactively, which is also called parallel type[9]. In this auxiliary management system, MySQL is used as the backend database to store information resources and support the operation of various functional modules, while for the user needs a powerful and easy-to-use tool, the B/S structure system can well meet the user requirements to implement and manage the process.

Figure 2

Database technology: Database technology is a data-based processing technology that provides the user with the required information by means of storage and calculation, as well as analysis and query. A large amount of original credential information is needed in the tennis sports assistance system, and the saving of relevant records can be completed when the parameters are entered. The data storage process is shown in Figure 3.

Figure 3

ASP.NET technology: ASP technology is a new type of online programming software, whose structure is shown in Figure 4. It is combined with traditional computer, it has powerful functional modularity, simple interface design without complicated operation and maintenance. The TCP/IP protocol is used for data transmission over the network, and the system encrypts and decrypts a large number of user names and passwords stored in the database through a background program[10]. The application can also provide users with various forms of input and output status or other styles of menu style, and it can also be flexible to set different types of menus according to the needs of users, so as to achieve a variety of functions.

Figure 4

Qualitative properties of the ordinary differential equations: the present system of plane polynomials can be expressed by equation (1). (1) dxdt=f(x,y),dydt=g(x,y) {{dx} \over {dt}} = f\left( {x,y} \right),{{dy} \over {dt}} = g\left( {x,y} \right)

Analyze the qualitative properties of the ordinary differential equation as follows:

First, analyze the finite singularity of the ordinary differential equation: if the point VVV satisfies both equation (2), then (x', y') is the singularity of this planar polynomial system. (2) f(x•,y•)=0, g(x•,y•)=0, f\left( {{x^ \bullet },\,{y^ \bullet }} \right) = 0,\,\,g\left( {{x^ \bullet },\,{y^ \bullet }} \right) = 0,\,

At this point, if the parameters a, b, c, d satisfy the equations (3) and (4), then this singularity is unique. (3) a=∂f∂x|x=x•,b= ∂f∂y|x=x•,c= ∂g∂x|x=x•,d= ∂g∂y|x=x• a = {{\partial f} \over {\partial x}}\left| {_{x = {x^ \bullet }},b = \,{{\partial f} \over {\partial y}}\left| {_{x = {x^ \bullet }},c = \,{{\partial g} \over {\partial x}}\left| {_{x = {x^ \bullet }},d = \,{{\partial g} \over {\partial y}}\left| {_{x = {x^ \bullet }}} \right.} \right.} \right.} \right. (4) | acbd |≠0 \left| {\matrix{ a \hfill & c \hfill \cr b \hfill & d \hfill \cr } } \right| \ne 0

The qualitative form of the system can be determined by the roots of the characteristic equation of the system (characteristic roots), which is shown in Equation (5). (5) | a−λbcd−λ |−y=0 {\left| {\matrix{ {a - \lambda } \hfill \cr b \hfill \cr } \matrix{ \hfill c \cr \hfill {d - \lambda } \cr } } \right|^{ - y}} = 0

Equation (6) can be obtained by transforming Equation (5). (6) λ2−(a+b)λ+ad−bc=0 {\lambda ^2} - \left( {a + b} \right)\lambda + ad - bc = 0

When λ₁, λ₂ is the same negative real root, the corresponding singularity is a stable node; when λ₁, λ₂ is the same positive real root, the corresponding singularity is an unstable node. In order to study the distribution of the trajectories over the full plane (global structure), it is also necessary to study the domain of infinitely far singularities. The parameter substitution is shown in Equation (7). (7) x=1/z,y=u/z x = 1/z,\,y = u/z

Systematizing equation (7) yields (8) as shown: (8) dudt=−uzf(1z,uz)+zg(1z,uz)dudt=−z2f(1z,uz) \matrix{ {{{du} \over {dt}} = - uzf\left( {{1 \over z},{u \over z}} \right) + zg\left( {{1 \over z},{u \over z}} \right)} \hfill \cr {{{du} \over {dt}} = - {z^2}f\left( {{1 \over z},{u \over z}} \right)} \hfill \cr }

Equation (8) can be transformed into Equation (9) by a generalization. (9) dudt=f•(u,z)zn,dzdt=g•(u,z)zn {{du} \over {dt}} = {{{f^ \bullet }\left( {u,z} \right)} \over {{z^n}}},\,{{dz} \over {dt}} = {{{g^ \bullet }\left( {u,z} \right)} \over {{z^n}}}

Further parameter substitution can be done to obtain equation (10). (10) dt=znd τ dt = {z^n}d\,\tau

Simplifying equation (10) yields equation (11). (11) dudt=f•(u,z),dudτ=g•(u,z) {{du} \over {dt}} = {f^ \bullet }\left( {u,z} \right),\,{{du} \over {d\tau }} = {g^ \bullet }\left( {u,z} \right)

Then the infinitely far singular point on the phase plane corresponds to (11) on the z = 0 axis on the Π plane, i.e., equation (12) is obtained. (12) f•(u,0)=0,g•(u,0)=0 {f^ \bullet }\left( {u,0} \right) = 0,{g^ \bullet }\left( {u,0} \right) = 0

Studying the field of D, D' on the equator, then the system is substituted by the parameters to obtain the equation (13). (13) x=v/z,y=1/z x = v/z,\,y = 1/z

The simplification leads to equation (14). (14) dvdt=zf(vz,1z)−zvg(vz,1z)dvdt=−z2g(vz,1z) \matrix{ {{{dv} \over {dt}} = zf\left( {{v \over z},{1 \over z}} \right) - zvg\left( {{v \over z},{1 \over z}} \right)} \hfill \cr {{{dv} \over {dt}} = - {z^2}g\left( {{v \over z},{1 \over z}} \right)} \hfill \cr }

The generalization leads to Equation (15). (15) dvdt=f••(v,z)zm,dzdt=g••(v,z)zm {{dv} \over {dt}} = {{{f^{ \bullet \bullet }}\left( {v,z} \right)} \over {{z^m}}},\,{{dz} \over {dt}} = {{{g^{ \bullet \bullet }}\left( {v,z} \right)} \over {{z^m}}}

Doing the parameter substitution yields Equation (16). (16) dt=zmdt dt = {z^m}dt

The simplification leads to equation (17). (17) dvdτ=f••(v,z),dzdτ=g••(v,z) {{dv} \over {d \tau}} = {f^{ \bullet \bullet }}\left( {v,z} \right),\,{{dz} \over {d\tau }} = {g^ \bullet }^ \bullet \left( {v,z} \right)

In traditional teaching, teachers teach students to learn, but the learning efficiency is very low, but the development of modern network technology allows us to solve these problems through the computer. The mobile support system can not only improve the classroom learning effect and interactivity, but also enhance the students' mastery of the course knowledge, and reduce the teacher's teaching burden, thus increasing the students' independent participation, so that they can complete the reception of their own interest in the course in a relaxed atmosphere[11].

Ordinary differential equation is a kind of linear function, which can be created according to the need of corresponding equation, but its solution is not uniquely determined, so when we analyze the problem, we often can not get the correct answer very well. The auxiliary system can solve the equation, which requires us to design a set of software and hardware suitable for teaching needs.

1) Function fode(t,x,z): find the first order equation x= F(t,x) of the vector field function, where t,x is the independent variable and the range of values of the function, z= F(t,x) for the vector direction function, the procedure is as follows:

function w=fode(t,x,z)

The function fodeivc (z, xO, y0, x1, x2, y1, y2): find the solution of the initial value problem CCC, where x0, y0 is the initial value, x1, x2, y1, y2 is the range of values of the initial value solution, the program is as follows:

function h=fodeivc(z, xO, yO, x1, x2, y1, y2)

The function todet(F,G,H,x0,y0,zO,t0,t1), whose system of equations is shown in Equation (18). (18) { dxdt=F(x,y,z)dydt=G(x,y,z)dxdt=H(x,y,z) \left\{ {\matrix{ {{{dx} \over {dt}} = F\left( {x,\,y,\,z} \right)} \hfill \cr {{{dy} \over {dt}} = G\left( {x,\,y,\,z} \right)} \hfill \cr {{{dx} \over {dt}} = H\left( {x,\,y,\,z} \right)} \hfill \cr } } \right.

F,G,H are the right end functions of the system of equations, x0,y0,z0 are the initial values, t0,t1 are the two end points of the solution interval of the differential equation, and the procedure is as follows:

function f=todet(a,b,c,x0,y0,z0,t0,t1)

When designing this support system, the following factors should be taken into account:

First of all, it is necessary to meet the basic needs of the user for learning tennis. The actual situation will determine what kind of model to use and how to make it. The second factor is whether the technology required for the hardware and software parts can be realized and whether the functions are perfect or not; finally, it is the rationality and scientificity of the design of the specific development process and the possible problems and solutions, so that the practical value of the auxiliary system can be truly reflected[12]. The system is designed to meet the basic functional requirements of the users for daily teaching, and it can provide users with efficient, convenient, accurate and real-time characteristics. Therefore, the overall design of the system is shown in Figure 5.

Figure 5

The tennis sports assistance system mainly consists of a sensing module and a cell phone APP, in which the sensing module mainly includes six-axis sensors, a microprocessor for low-power wireless communication with smart phones and a power supply module. The cell phone APP collects motion signals in real time, analyzes and displays motion results.

Figure 6

The sensing module is a very important component in the system design. It is not only required to provide enough complete and reliable data information for the whole system, but also requires good reliability and security to ensure the normal operation of the machine or software used in the whole project development process. Characteristic parameters (e.g., hardware environment) can be captured and saved as a reference for the next stage of work, while also taking into account the need to simplify the structure and modularity as much as possible to improve system performance during design. The structure of the sensor module is shown in Figure 7.

Figure 7

At present, some universities in China have their own corresponding tennis sports assistance systems, but these functions only stay at the theoretical level and do not get enough attention, so further development is needed in the software. With the coming of the Internet era, mobile devices have become indispensable tools for people to get information, share information and communicate, and so on, and the tennis sports assistance system also comes into being. However, it is seldom applied to teaching in many universities in China, which leads to students' lack of deep understanding and mastery of the course, and the lack of teachers and hardware facilities, as well as the lack of attention to the technology in some schools, these have caused a serious lack of tennis courts and low quality, so it cannot meet the teaching needs of tennis. This paper presents a detailed analysis of the auxiliary system based on the design and implementation of the ordinary differential equation auxiliary system, which proposes and establishes a set of tennis mobile equipment management mode that is suitable for China's national conditions and can improve students' learning interest and experience effect.