Trajectory Simulation and Optimization of Bench-Dragon Dance Based on Spiral Motion Principles

The Bench-Dragon dance, a traditional cultural performance originating from the Zhejiang and Fujian regions of China, is renowned for its intricate spiral movements executed within confined spaces. This study seeks to enhance the performance's safety and aesthetic appeal through the development of a mathematical model based on Archimedean spiral equations and kinematic principles to simulate and optimize the dance trajectory. The model represents the dragon as a series of interconnected segments following a precisely defined spiral path. To address the common issue of segment overlap, which disrupts performance fluidity in limited spaces, a collision detection algorithm is incorporated.Extensive numerical simulations are conducted to analyze the behavior of each segment and dynamically adjust the trajectory to maintain optimal spacing. The results indicate that this model effectively reduces the risk of collisions, enhances synchronization, and contributes to the visual harmony of the performance. This approach demonstrates potential applications in other traditional dances or choreographed group movements requiring precise coordination. By integrating modern optimization techniques, the study provides a valuable tool for preserving cultural heritage while refining and elevating traditional performances.