基于几何模型的舞龙队位置和速度分析  

Geometric Model Based Position and Velocity Analysis of Dragon Dance Team

作　　者：李俊凯 朱予彤 张宇君 LI Junkai;ZHU Yutong;ZHANG Yujun(College of Information Engineering,Zhejiang University of Technology,Hangzhou,Zhejiang 310023,China;School of Computer Science and Technology,Zhejiang University of Technology,Hangzhou,Zhejiang 310023,China)

机构地区：[1]浙江工业大学信息工程学院,浙江杭州310023 [2]浙江工业大学计算机科学与技术学院,浙江杭州310023

出　　处：《数学建模及其应用》2025年第1期58-66,共9页Mathematical Modeling and Its Applications

摘　　要：本研究以民俗活动板凳龙为背景,建立了板凳龙运动的几何模型,并利用向量和矩阵简化了建模和计算过程.首先,基于等距螺线方程,建立了把手位置和速度的计算模型,并通过逐步逼近法求解极角,得到把手位置和速度的求解方法.其次,定义了碰撞条件,通过向量分析和碰撞检测模型,确定了易碰撞点的碰撞时刻.接着,通过调整螺距和步长,计算出螺距的最小值.此外,对调头区域的几何关系进行了分析,发现调头曲线长度不变,并通过构建矩阵,分析了龙头前把手的位置和速度.最后,证明了把手速度变化的一致性,计算出龙头的最大行进速度.In this paper,the geometrical model of bench dragon motion is established with the background of the folklore activity bench dragon,and the modelling and calculation process is simplified by using vectors and matrices.Firstly,based on the equidistant solenoidal equation,the computational model of the handle position and velocity is established,and the solution of the handle position and velocity is obtained by solving the polar angle through the step-by-step approximation method.Secondly,the collision conditions were defined,and the collision moments of the collision-prone points were determined by vector analysis and collision detection model.Next,the minimum value of pitch was calculated by adjusting the pitch and step size.In addition,the geometrical relationship of the header region was analyzed and it was found that the length of the header curve was constant,and the position and velocity of the handle in front of the tap were analyzed by constructing a matrix.Finally,the consistency of the change in handle velocity was demonstrated and the maximum travelling speed of the tap was calculated.

关 键 词：等距螺线方程 几何分析 逐步逼近法 碰撞检测模型 构建矩阵 

分 类 号：O29[理学—应用数学]