On Determining the Equation of a Salkowski Curve Satisfying tau/kappa=1/s

  • Yun Myung Oh Andrews University
  • Devin Garcia-Roblero Andrews University
DOI: https://doi.org/10.46787/pump.v6i0.2633
Keywords: Salkowski curve; Fundamental Theorem of Curves; Frenet-Serret equations

Abstract

In this paper, we determine the equation of a Salkowski curve whose ratio of torsion to curvature is given by 1/s, where s is the arc length of the curve. The Frenet-Serret equations provide the third-order vector differential equation for the unit tangent vector T(s) and the general (series) solution was obtained. In the end, the series solution is entirely determined by the given initial conditions.

Author Biography

Yun Myung Oh, Andrews University

I am a professor in the Department of Mathematics at Andrews University and have been working here since 2006. Devin Garcia-Roblero was a freshman when we worked on this project. He was very enthusiastic about doing the research and did a wonderful job. 

Published
2023-11-28
How to Cite
Oh, Y. M., & Garcia-Roblero, D. (2023). On Determining the Equation of a Salkowski Curve Satisfying tau/kappa=1/s. The PUMP Journal of Undergraduate Research, 6, 346-353. https://doi.org/10.46787/pump.v6i0.2633
Issue
Vol. 6 (2023): PUMP Journal of Undergraduate Research
Section
Articles

Copyright (c) 2023 Yun Myung Oh, Devin Garcia

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