An Integrated Approach of The Brachistochrone And Tautocrone Curve

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2020 by IJMTT Journal
Volume-66 Issue-12
Year of Publication : 2020
Authors : Dhruv Sharma
  10.14445/22315373/IJMTT-V66I12P503

MLA

MLA Style: Dhruv Sharma  "An Integrated Approach of The Brachistochrone And Tautocrone Curve" International Journal of Mathematics Trends and Technology 66.12 (2020):17-22. 

APA Style: Dhruv Sharma(2020). An Integrated Approach of The Brachistochrone And Tautocrone Curve  International Journal of Mathematics Trends and Technology, 17-22.

Abstract
The Brachistochrone and Tautocrone problem is not new but it was one of the fundamental problems given to the best mathematical minds in the world like Bernoulli brothers, L-hopital, Newton and Gottfried Leibnitz. As an enlightening fact the problem was both given and cracked by Johann Bernoulli. This was not just the foremost mathematical problem in the world but also the instigator of the branch of mathematics called as “Calculus of variation” and also proved many physical prodigies so, in essence this problem marked a breakthrough in the world of science. I have developed an approach based on the parity of both the Brachistochrone and Tautocrone curve that syndicates both of them which can further lead to mathematical progressions or can make new progresses in the field of physics.

Reference

[1] G. Korn, T. Korn, Mathematical Handbook, McGraw-Hill, New York 1968.
[2] Charles Fox, An introduction to the calculus of variations.
[3] Cornelius Lanczos, The variational principles of mechanics.
[4] Terra, Pedro & Souza, Reinaldo & Farina de Souza, Carlos. (2016). Is the tautochrone curve unique? American Journal of Physics. 84. 10.1119/1.4963770. https://www.researchgate.net/publication/308883905_Is_the_tautochrone_curve_unique
[5] Parnowski, Aleksei. (1998). Some generalisations of brachistochrone problem. 93. S-55. https://www.researchgate.net/publication/298004003_Some_generalisations_of_brachistochrone_problem
[6] Nishiyama, Yutaka. (2013). The brachistochrone curve: The problem of quickest descent. International Journal of Pure and Applied Mathematics. 82. 409-419.
[7] Gómez, Raúl & Marquina, Vivianne & Gómez-Aíza, S. (2008). An alternative solution to the general tautochrone problem. Revista mexicana de física E. 54. https://www.researchgate.net/publication/237694649_An_alternative_solution_to_the_general_tautochrone_problem
[8] Terra, Pedro & Souza, Reinaldo & Farina de Souza, Carlos. (2016). Is the tautochrone curve unique? American Journal of Physics. 84. 10.1119/1.4963770. https://www.researchgate.net/publication/308883905_Is_the_tautochrone_curve_unique
[9] Aleksandra Risteska, Application of Fundamental Lemma of Variational Calculus to the Problem for the Brachistochrone, International Journal of Mathematics Trends and Technology (IJMTT). V57(5):296-302 May 2018. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Keywords : Brachistochrone Cycloid, Descend, Gravity, Shortest path, Tautochrone