“板凳龙”的螺线运动分析与求解  

Kinematic Analysis and Solution to Spiral Maneuvers in“Bench Dragon”

作　　者：王吉彬 倪力赟 于明硕 WANG Ji-bin;NI Li-yun;YU Ming-shuo(Zhang Jian College,Nantong University,Nantong 226019,China;School of Physical Science and Technology,Nantong University,Nantong 226019,China)

机构地区：[1]南通大学张謇学院,江苏南通226019 [2]南通大学物理科学与技术学院,江苏南通226019

出　　处：《南通职业大学学报》2025年第1期60-64,93,共6页Journal of Nantong Vocational University

基　　金：江苏省教育厅省高校面上项目(24KJB520033);南通大学2023年度教学改革研究课题(2023C07)。

摘　　要：针对“板凳龙”在龙头速度恒定时沿等距螺线盘入和盘出的相关运动问题,基于理论力学极坐标系下的速度变换,分析得到在不同等距螺线下每个板凳的位置坐标及速度;并由此建立平面刚体碰撞检测模型,以判断板凳间是否发生碰撞;再利用二分搜索算法求解进入调头区域前不发生碰撞的最小螺距;通过几何分析证明了调头曲线长度为定值,并确定舞龙队的盘入、盘出路线;最后,建立最大龙头速度单目标优化模型,采用二分搜索算法求出龙头最大行进速度。The kinematic issues of the“Bench Dragon”formation during spiraling-in and spiraling-out from equidistant spirals with a constant leading speed are addressed.Based on velocity transformation in the polar coordinate system of theoretical mechanics,the position coordinates and velocities of each bench under various equidistant spirals are analyzed and derived.Then a planar rigid body collision detection model is established to identify potential collisions between benches,with the binary search algorithm employed to determine the minimum pitch required to prevent collisions before entering the turning zone.Geometric analysis proves that the turning curve length remains constant,thereby the spiraling-in and spiraling-out trajectories for the dragon dance team is determined.Finally,a single-objective optimization model for maximum dragon head velocity is developed,and the binary search algorithm is used to calculate the maximum achievable velocity of the dragon head.

关 键 词：等距螺线 极坐标系 速度变换 二分搜索算法 单目标优化模型 “板凳龙” 

分 类 号：O311[理学—一般力学与力学基础]