Research on bench dragon motion based on Runge-Kutta algorithm

Xiaoou Bai; Kangrong Shi; Zihao Bai; Haohang Wen

doi:10.54097/xe4f9822

Authors

Xiaoou Bai
Kangrong Shi
Zihao Bai
Haohang Wen

DOI:

https://doi.org/10.54097/xe4f9822

Keywords:

Differential Equation, Runge-Kutta Algorithm, SAT Crash Test, Cosine iterative method.

Abstract

"The Bench Dragon" is a distinctive folk art form originating from the Fujian and Zhejiang regions of China. It plays a pivotal role in cultural preservation and serves as a vital conduit for cultural exchange, both within China and globally. A well-executed "Bench Dragon" performance significantly bolsters national cultural identity and is a prominent display of China's cultural allure. The study focuses on enhancing the performance's fluidity and safety by precisely determining the real-time location of the dragon dance team and anticipating potential collisions. The research employs a mathematical approach to model the dragon's movement as a spiral curve, utilizing differential equations and the Runge-Kutta algorithm to describe the position of the dragon head's front handle at any moment. This methodological innovation offers a scientific basis for the performance, optimizing it through mathematical modeling to improve both its visual appeal and safety. Additionally, the cosine iteration method is applied to calculate the positions of the dragon body and tail handles, based on the known position of the head's front handle, ensuring the performance's synchronicity. The study also delves into the analysis of potential collisions using the SAT algorithm, which, after simplifying the judgment criteria, accurately forecasts the timing of collisions. This analysis is crucial for ensuring the performance's safety and smooth progression. The integration of mathematical and physical sciences with the "Bench Dragon" tradition not only enriches its research domain but also provides novel scientific methodologies and technical support for the continuation and evolution of this traditional folk art. This interdisciplinary approach underscores the potential for blending traditional practices with modern scientific techniques to foster cultural heritage while ensuring performances are conducted with enhanced safety and aesthetic quality.

Downloads

Download data is not yet available.

References

[1] Pan D, Sirisuk M. Collective Memory Construction and Educational Inheritance of Ritual Practices of Bench Dragon Performance in Pujiang, China: Educational Inheritance of Ritual Practices of Bench Dragon Performance[J]. International Journal of Curriculum and Instruction, 2023, 15(3): 2232-2250.

[2] Pan D, Sirisuk M. Bench Dragon Performance at Pujiang, Zhejiang Province: The Overlapping in-between the Ritual Practice and Intangible Cultural Heritage Management of China[D]. Mahasarakham University, 2023.

[3] Folland G B. Introduction to partial differential equations[M]. Princeton university press, 2020.

[4] Teschl G. Ordinary differential equations and dynamical systems[M]. American Mathematical Society, 2024.

[5] Ahmadianfar I, Heidari A A, Gandomi A H, et al. RUN beyond the metaphor: An efficient optimization algorithm based on Runge Kutta method[J]. Expert Systems with Applications, 2021, 181: 115079.

[6] Linders V, Nordström J, Frankel S H. Properties of Runge-Kutta-summation-by-parts methods[J]. Journal of Computational Physics, 2020, 419: 109684.

[7] Zhang M, Bai H, Zhang J, et al. Rkformer: Runge-kutta transformer with random-connection attention for infrared small target detection[C]//Proceedings of the 30th ACM International Conference on Multimedia. 2022: 1730-1738.

[8] Gan B, Dong Q. An improved optimal algorithm for collision detection of hybrid hierarchical bounding box[J]. Evolutionary Intelligence, 2022, 15(4): 2515-2527.

[9] Chang J W, Wang W, Kim M S. Efficient collision detection using a dual OBB-sphere bounding volume hierarchy[J]. Computer-Aided Design, 2010, 42(1): 50-57.

[10] Procesi C. The rectangle graph[J]. arXiv preprint arXiv:2411.01334, 2024.