Research on Simulation of Multi-node Motion States of the Bench Dragon Based on Archimedean Spiral and ode45 Algorithm

In this study presents a groundbreaking simulation analysis of the multi-node motion states of the Bench Dragon, a cherished traditional Chinese folk activity. By seamlessly integrating Archimedean spiral theory with the ode45 algorithm, we systematically investigated the motion equations governing the Bench Dragon's movements along diverse paths. Focusing on a specific scenario where the dragon dance team progresses clockwise along an isometric spiral with a constant pitch of 55 cm, while maintaining a uniform speed of 1 m/s at the dragon head's front handle, we meticulously determined the dragon head's positional changes on the spiral using parametric equations and velocity decomposition. Leveraging the cosine theorem and iterative approximation techniques, we further derived the precise positions and velocities of subsequent nodes, encompassing both the body and tail handles. Numerical solutions were obtained by employing MATLAB's ode45 function to solve the underlying differential equations. Our findings provide comprehensive spatial coordinates and instantaneous speeds for pivotal nodes at multiple time points, offering profound insights into the dynamic stability and coordination of traditional Bench Dragon dances. This research not only deepens our comprehension of complex kinematic behaviors in cultural performances but also embodies a methodological innovation by intertwining mathematical modeling with cultural heritage studies. The proposed framework holds promising applications across diverse fields, including computer animation, sports training, and the preservation of cultural heritage.