基于二分法对等距螺线板凳龙的优化分析

Optimization Analysis of Equidistant Spiral Bench Dragon Based on Dichotomous Method

摘要: 本文通过建立一系列数学模型来分析和优化其运动过程，研究涵盖板凳龙的盘入、调头和盘出等阶段，涉及几何学、运动学、优化理论等多个数学领域。综合运用多种数学工具和计算方法，通过微分方程、动态碰撞模型、螺距优化模型、曲线优化模型、动态速度约束优化模型成功解决了运动轨迹规划、碰撞检测、螺距优化、调头路径设计和速度控制等问题，为提高板凳龙表演的观赏性、安全性和技术难度提供了理论基础和实践指导。

Abstract: This paper analyzes and optimizes the motion process by establishing a series of mathematical models, covering the stages of disc entry, turning and disc exit of the bench dragon, involving geometry, kinematics, optimization theory and other mathematical fields. By comprehensively using a variety of mathematical tools and calculation methods, the problems of motion trajectory planning, collision detection, pitch optimization, U-turn path design and speed control were successfully solved through differential equations, dynamic collision models, pitch optimization models, curve optimization models, and dynamic velocity constraint optimization models, which provided theoretical basis and practical guidance for improving the ornamentality, safety and technical difficulty of bench dragon performances.