166
Views
0
CrossRef citations to date
0
Altmetric
Classroom Notes

The brachistochrone problem revisited: a numerical solution via non-linear root-finding

, , &
Pages 3417-3427 | Received 21 May 2021, Published online: 06 Oct 2021

References

  • Albright B., & Fox W. P. (2020). Mathematical modeling with Excel (2nd ed.). CRC Press.
  • Babb J., & Currie J. (2008). The brachistochrone problem: Mathematics for a broad audience via a large context problem. The Montana Mathematics Enthusiast, 5(2-33), 169–183.
  • Burden R. L., Faires J. D., & Burden A. M. (2016). Numerical analysis (10th ed.). Cengage Learning.
  • Coleman R. (2012). A detailed analysis of the brachistochrone problem, Preprint. arXiv:1001.2181v2.
  • Erlichson H. (1999). Johann Bernoulli's brachistochrone solution using Fermat's principle of least time. European Journal of Physics, 20 (5), 299–304. https://doi.org/10.1088/0143-0807/20/5/301
  • Freguglia P., & Giaquinta M. (2016). The early period of the calculus of variations. Birkhäuser.
  • Henrici P. (1964). Elements of numerical analysis. Wiley.
  • Posamentier A. S., & Krulik S. (1998). Problem-solving strategies for efficient and elegant solutions: A resource for the mathematics teacher. Corwin Press.
  • Sahab M. G., Toropov V. V., & Gandomi A. H. (2013). A review on traditional and modern structural optimization: Problems and techniques. In A. H. Gandomi, X. S. Yang, S. Talatahari, & A. H. Alavi (Eds.), Metaheuristic applications in structures and infrastructures (pp. 25–47). Elsevier.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.