Papers by Keyword: Runge-Kutta Method

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Authors: Meng Qi Ma, Fang Ping Lei, Yu Qiao Ren, Bai Song Mu
Abstract: A method of establishing a kinematic model for simulated railroad freight car impact based on the Runge-Kutta method is introduced in this paper. The model is solved based on numerical analysis to obtain the relationship of variables, furthermore providing a basis for determining the loading support and loading securement method.
Authors: Ding Xuan Zhao, Ying Jie Li, Guo Jun Yang, Qing Bo Hao, Gang Liu, Miao Xu
Abstract: Dynamics model of fighter was proposed in order to drive on flight simulator virtually. The model took Lagrange equation as basis and simplified analysis of the force on fighter according to the real-time input state information from joystick. The dynamics equation was solved in real time using Runge-Kutta method (RK4). It was proved finally that the model and simulation algorithm had higher dependability through datum and simulation scene which was obtained with graphics engine OpenGVS and 3D visual modeling Software Multigen Creator.
Authors: Zhu Li Wu
Abstract: This paper introduces Runge-Kutta method into the game decision model of advertising differential equation, and establishes the two-order Runge-Kutta and the four-order Runge-Kutta differential equation models to study the impact of new fashion product on the sales and the impact of supply chain on the overall performance. In order to verify the validity and reliability of the model, this paper uses the MATLAB software to design the algorithm of advertising promotion differential equation model, and gets the accounting system of three types of advertising sales, and uses this system to statistics the sales. From the results we can see, the popular goods and seasonal goods have the largest effect on the new development fashion goods sales in three types of advertising, so it should increase the advertising delivery in popular goods and seasonal goods to ensure the sales of new fashionable goods.
Authors: Wei Guo Zhu, Xiang Zhong Bai
Abstract: The problem of bifurcation and chaos in a 4-side simply supported rectangular thin electro-magneto-elastic plate in electro-magnetic, mechanical and temperature fields is studied. Based on the basic nonlinear electro-magneto-elastic motion equations for a rectangular thin plate and expressions of electromagnetic forces, vibration equations are derived for the mechanical loading in a nonlinear temperature field and a steady transverse magnetic field. By using Melnikov function method, the criteria are obtained for chaos motion to exist as demonstrated by the Smale horseshoe mapping. The vibration equations are solved numerically by using a fourth-order Runge-Kutta method. Its bifurcation diagram, Lyapunov exponents diagram, displacement wave diagram, phase diagram and Poincare section diagram are obtained for some examples. The characteristics of the vibration system are analyzed, and the roles of parameters on the systems are discussed separately as well, such as electromagnetic field intensity, temperature and mechanical force.
Authors: A.K. Mishra, N. Senapati, S.R. Mishra, S. Bhattacharjee
Abstract: The purpose of this paper is to investigate steady two-dimensional laminar magnetohydrodynamic (MHD) flow of an incompressible Jeffrey fluid past over a linearly stretching sheet. The governing partial differential equations (PDEs) of continuity, momentum, energy and concentration are transformed into nonlinear coupled ordinary differential equations (ODEs) by using similarity transformations. Then the ODEs are solved by applying Runge-Kutta fourth order method accompanied with shooting technique. The effects of various physical parameters characterizing the flow phenomenon including Deborah number, ratio of relaxation to retardation times, magnetic parameter, porous parameter, Prandtl number, Eckert number, heat source / sink parameter, Schmidt number and chemical reaction parameter on dimensionless velocity, temperature and concentration profiles are analyzed. The numerical results are obtained and presented in graphs. The present results are compared with the earlier published results as a particular case.
Authors: Xin Zhang, Lan Yu
Abstract: Obtaining the flight attitude of high accuracy, high reliability is a prerequisite for achieving the autonomous flight of the multi-rotor UAV. MEMS gyroscope can solve attitude angle individually. The paper adopts Euler angle and quaternion algorithms respectively to calculate attitude angle of the multi-rotor UAV. The flight experiment shows that the quaternion algorithm can guarantee the accuracy and the stability of the attitude angle calculation. The root-mean-square errors of the pinch roll and heading angles which are calculated by the quaternion algorithm are 2.947o, 3.606o and 9.769o, which can meet the demand for the autonomous flight of the multi-rotor UAV.
Authors: Yu Hui Xie, Lei Zhang, Xue Zheng Huang
Abstract: Based on the mass action law, the kinetics equation of the complex consecutive reaction was established in the form of first-order ordinary differential equations. Therefore; a program was designed by the Visual Basic language and the theory of the numerical calculation to solve the ordinary differential equations. In the end, the reaction process of the complex consecutive reaction was simulated by the powerful plot function of the Visual Basic language.
Authors: Jun Guo Li, Hong Wei Lu, Yu Zhu Zhang
Abstract: After gas quenching and granulated, the molten steel slag changed into droplets. The cooling and solidification process of the droplets have been analyzed and calculated in this paper. It was suggested that there were three phases such as liquid cooling phase, nucleation and recalescence phase, and solid cooling phase. During the cooling process, there were two heat transfer modes such as convection and radiation from droplets surface to environment. On the other hand, there was a great amount of latent heat released during nucleation and solidification process. The physical model of droplets cooling has been established on the basis of heat transfer theory. And then the mathematic model with nonlinear ordinary differential equations could be extracted, which could be solved through fourth-order Runge-Kutta method. The declining law of droplets temperature along with the cooling time could be drawn by Matlab software. It takes 249ms, 83ms and 185ms for liquid cooling, nucleation and recalescence and solid cooling phase, respectively. In conclusion, it takes about 332ms to solidify entirely for the droplets, and 517ms to be cooled from 1723 to 1073K.
Authors: Xiang Zhen Xue, San Min Wang
Abstract: As one of the important components of aviation and space transmission systems, dynamic characteristics of involute spline couplings influence its lifetime and reliability seriously. Here, taking the backlash of spline joint into account, considering the meshing stiffness varying with the teeth engaged, established the dynamic model with varying stiffness and dynamic equations, and calculated the number of actual meshing teeth and comprehensive meshing stiffness while bearing the varying torque, then, solved dynamic equations using the fourth order Runge - Kutta method, finally, get the teeth meshing number is 23,and the maximum dynamic load coefficient gets smaller from 1.19 to1.15 with the decrease of . This provides a numerical basis for wear`s studying and lifetime`s forecasting of involute spline coupling.
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