Dynamic Simulation and Optimization Study Based on Archimedean Solenoidal Motion and Collision Detection Models

In this paper, the motion characteristics of the traditional folk dance "bench dragon" are taken as an example, and tools from several mathematical fields such as geometry, kinematics, optimization theory and numerical analysis are comprehensively applied to study the motion state of the object by solving differential equations, dynamic collision detection and optimal control theory [1],[2]. First, the differential equations describing the motion of the dragon's head are solved by the Runge-Kutta method based on the Archimedean spiral equation, and the positions of the parts of the dragon's body and tail are deduced from the connectivity relations [3],[4]. The speed calculation uses the central difference method to iteratively simulate the motion process of the dragon dance team per second, and improves the efficiency by vectorization calculation. Next, a dynamic collision detection model is introduced to abstract the collision between benches into a rectangular collision problem. The safety and smoothness of the dragon dance performance are further ensured by gradually calculating the position of each bench and checking the collision with the benches with defined positions in real time. These research results provide an important theoretical basis and practical guidance for the study of complex and variable motion states.