Research On Real Time Simulation Algorithm Of Discontinuous Dynamic System Based On Piecewise Processing

In this paper,the real-time simulation algorithm of discontinuous dynamics system is studied.Conventional numerical simulation algorithm cannot handle the discontinuous interval well when the discontinuous dynamics system is simulated in real-time.In this paper,a real-time simulation algorithm of discontinuous dynamic system based on piecewise processing is proposed,and the idea of discontinuous interval being divided into two segments is proposed.The fifth-stage fourth-order real-time continuous Runge-Kutta(R-K)formula was used to predict the breaking points,and the Hermite interpolation polynomial was constructed to find out the breaking points.The intervals were divided into two sections by taking the breaking points as the boundary,and the two sections were calculated by using the second-order R-K formula.The step length of two intervals is calculated by the proportion of the break point in the interval,which ensures that the step length of the interval is the same as that of the continuous interval and satisfies the requirement of real-time simulation.The algorithm is simple in structure and small in computation.In this paper,the method of Brent was used to solve the root of Hermite interpolation formula,and the root of Hermite interpolation formula was used to replace the break point.After that,the two-dimensional model of multi-ball collision and three-dimensional model of multi-ball collision were established to analyze the situation of multi-ball collision in detail,the real-time simulation algorithm is used to calculate the multi-ball collision model and realize the visualization of the two-dimensional model of multi-ball collision.The main research contents of this paper are as follows:(1)In chapter 1,the research background and significance of real-time simulation algorithm are described.(2)In chapter 2,this chapter introduced the basic theory of constructing real-time simulation algorithms,introduced the Hermite interpolation polynomial,and explained the derivation process from first-order R-K formula to fourth-order R-K formula in detail.(3)In chapter 3,a real-time simulation algorithm of discontinuous dynamics based on piecewiseprocessing is constructed.The classification of discontinuity problems is summarized and the concrete steps of real-time simulation algorithm are introduced in detail.(4)In chapter 4,the principle of the method of Brent is introduced,the real-time simulation algorithm constructed in this paper is used to calculate the free-falling motion model and analyze its errors.(5)In chapter 5,the two-dimensional model and three-dimensional model of multi-ball collision are established,and the real-time simulation algorithm constructed in the third chapter is used to calculate the two-dimensional model and three-dimensional model of multi-ball collision.In the real-time simulation calculation of two-dimensional model and three-dimensional model of multi-ball collision,multiple sets of simulation were carried out respectively to clearly analyze the velocity and position information of each ball,and then the visualization of two-dimensional model was made according to the calculated position and velocity information.The simulation results did not show the phenomenon of the balls crossing the boundary and the overlap between the balls.It shows that the real-time simulation algorithm proposed in this paper can achieve the expected effect.It is proved that the real-time simulation algorithm can be applied to the two-dimensional model and three-dimensional model of multi-ball collision.