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.

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.

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.

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.

Qualitative properties of the ordinary differential equations: the present system of plane polynomials can be expressed by equation (1).

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.

At this point, if the parameters a, b, c, d satisfy the equations (3) and (4), then this singularity is unique.

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).

Equation (6) can be obtained by transforming Equation (5).

When _{1}, _{2} is the same negative real root, the corresponding singularity is a stable node; when _{1}, _{2} 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).

Systematizing equation (7) yields (8) as shown:

Equation (8) can be transformed into Equation (9) by a generalization.

Further parameter substitution can be done to obtain equation (10).

Simplifying equation (10) yields equation (11).

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.

Studying the field of D, D' on the equator, then the system is substituted by the parameters to obtain the equation (13).

The simplification leads to equation (14).

The generalization leads to Equation (15).

Doing the parameter substitution yields Equation (16).

The simplification leads to equation (17).

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)

[t,x]=meshgridt,x);dt=ones(size(t));

dx=eval(z);quiver(t,x,dt,dx)

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)

syms x y;

F=[’Dy=’z];

y=dsolve(F, ’y(x0)=y0’,’x’);

x=x1:0.1:x2;

y=eval(y);

plot(x,y, r);

The function todet(F,G,H,x0,y0,zO,t0,t1), whose system of equations is shown in Equation (18).

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)

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

p=@(t,x)[eval(a);

eval(b);eval(c)];

u0=[x0;y0;z0];

[t,x]=ode45(p,[t0,t 1 ],u0);

figure(1);

plot(t,x);figure(2)

plot3(x(:,1),x(:,2),x(:,3));

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.

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.

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.

System development mainly includes two parts: hardware environment and software environment, of which hardware conditions are the most important part of the whole project. In this set of program design process, in order to facilitate the testing, debugging and maintenance of the modules need to choose the appropriate development tools and complete the corresponding functions; the system selected the more common and highly portable MyEclipse as the central chip to achieve development. Database as a complete architecture built up is the software platform contains and supports the entire application running requirements, it is one of the important components of the program design process. Database applications are at the core of the entire software system, a good program should not only have excellent and reliable storage and delivery of data functions, but also have a good generality of high, easy to use features.

System performance evaluation is the basis for evaluating the entire project. By testing this functional item, user requirements can be understood and the software can be improved and refined. In order to improve the system performance index: throughout the development process, it is necessary to constantly check whether the equipment used meets the user requirements. This is not only to consider the factors of the product itself, hardware conditions and other issues, but also to fully consider the degree of impact of changes in customer needs and other external environments, and also to focus on whether the product can provide better service or support to cope with the unpredictability of changes that occur in a variety of situations.

The design of a tennis auxiliary system based on ordinary differential equations is centered on user requirements, and the corresponding functional modules are created in the database for management and maintenance. According to the requirements of this system design, each component is described in detail, including auxiliary equipment, management interface and database modules.

In the system evaluation process, the development and operation efficiency of the software were mainly measured. For this auxiliary teaching aid, whether its performance meets the user's needs and whether the usage time can be satisfied will be the important criteria to evaluate the system. Therefore, it is necessary to realize the interactivity, collaboration and portability between the tennis mobile learner and traditional teaching aids through relevant technical means, and it is necessary to evaluate and analyze the problems encountered in the development process of the whole system to ensure the improvement of the software design quality; secondly, through the design of this auxiliary tool, the operation efficiency of the whole system can be improved, and it can promote the improvement of the tennis mobile teaching software to a certain extent.

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.

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Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Research on threat assessment problems of island air defence system based on the leader-follower model Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model