“板凳龙” 调头区域优化分析  

Optimization Analysis of the"Bench Dragon"Turnaround Area

作　　者：吴铭威 齐丞英 张丁元 WU Mingwei;QI Chengying;ZHANG Dingyuan(School of Mathematics and Statistics,Shandong University(Weihai),Weihai,Shandong 264209,China)

机构地区：[1]山东大学(威海)数学与统计学院,山东威海264209

出　　处：《数学建模及其应用》2025年第1期49-57,共9页Mathematical Modeling and Its Applications

摘　　要：以2024年“高教社杯”全国大学生数学建模竞赛A题为背景,建立“板凳龙”在调头过程中的数学模型,研究“板凳龙”在调头过程中调头区域受两圆弧比例的影响,并探究调头区域最小半径的影响因素.进一步,根据相关结论,在保证路线美观与演出难度的前提下,比较得出相对最优的调头曲线.最后综合分析调头过程受螺距、板长等因素的影响,并给出相关数据结果.This paper takes the problem A of 2024 CUMCM as the background,establishes the mathematical model of the"bench dragon"in the turning process,studies the influence of the ratio of two arcs on the turning area of the"bench dragon"in the turning process,and explores the factors affecting the minimum radius of the turning area;Further based on relevant conclusions,while ensuring the beauty of the route and the difficulty of the performance,a relatively optimal turning curve can be compared and obtained;Finally,a comprehensive analysis was conducted on the influence of factors such as pitch and plate length on the turning process,and relevant data results were provided.

关 键 词：仿真模拟 二分法 平面几何 数学建模 

分 类 号：O29[理学—应用数学]