Quantitative Analysis and Application of The Bench Dragon's Movement on An Archimedean Spiral

Yubo Liao; Shuaihao Zhang; Xinyi Ning; Lingyu Chen; Li Liang

doi:10.54097/0nn7hh74

Authors

Yubo Liao
Shuaihao Zhang
Xinyi Ning
Lingyu Chen
Li Liang

DOI:

https://doi.org/10.54097/0nn7hh74

Keywords:

Archimedean Spiral, Differential Equation, Finite Difference Methods, Runge-Kutta.

Abstract

To optimize the kinematic parameters of the "Bench Dragon" in Chinese folk culture, it is requisite to establish a mathematical model to conduct real-time simulation of the motion state of the Bench Dragon when it moves along the Archimedean Spiral. At present, there are relatively few related studies on such issues. Thus, in this paper, by utilizing the properties of the Archimedean Spiral and differential equations in the polar coordinate system, a mathematical motion model of the "Bench Dragon" is established. The model is solved by employing the Runge-Kutta Method and the Finite Difference Method, obtaining the velocity and position of the "Bench Dragon" when it moves along the trajectory of the Archimedean Spiral. Simultaneously, this model is also applicable to deducing the real-time motion state of other chain-like objects moving along the Archimedean Spiral, and holds significant guiding significance for the design and operation of objects involving chains or link structures.

Downloads

Download data is not yet available.

References

[1] Chuanwen Liu. Research on the Inheritance and Development of Pujiang Bench Dragon from the Perspective of Cultural Confidence [J]. New Chu Culture, 2024, (31): 85-88.

[2] Archimedean Spiral [J]. New Century Intelligence, 2024, (45): 49.

[3] Zhong Y, Li W, Wu L, et al.High focusing efficiency plasmonic vortex based on archimedes spiral slot[J].Optics Communications, 2025, 577131433-131433.

[4] Zhu L H. A new method for researching differential equations[J]. Partial Differential Equations in Applied Mathematics, 2025, 13101050-101050.

[5] Boda L, Faragó I.New efficient numerical methods for some systems of linear ordinary differential equations[J]. Mathematics and Computers in Simulation, 2025, 230438-455.

[6] Eduardo S, M. A V, Ángel G, et al.Complex Ginzburg–Landau Equation with Generalized Finite Differences[J]. Mathematics, 2020, 8(12):2248-2248.

[7] Pan K, Wang P, Xu Y, et al.Combined compact finite difference schemes for 2-D acoustic wave propagation[J]. Journal of Applied Mathematics and Computing, 2025, (prepublish):1-27.

[8] Soga K. Finite Difference Methods for Linear Transport Equations with Sobolev Velocity Fields[J]. Journal of Mathematical Fluid Mechanics, 2024, 27(1):6-6.

[9] Cui Y, Yu Y, Liu Y, et al.An Approach Problem for Control Systems Based on Runge–Kutta Methods[J]. Computational Mathematics and Mathematical Physics,2024, 64(9):1991-2004.

[10] Hu X, Cong Y, Hu G. Delay-dependent stability of Runge–Kutta methods for linear delay differential algebraic equations[J]. Journalof Computational and Applied Mathematics, 2020, 363300-311.