A generalization of the Bernoulli’s method applied to brachistochrone-like problems
Makaleler > Tam Makale · 2013
Yazarlar: U. FILOBELLO-NINO, H. VAZQUEZ-LEAL, D. PEREYRA-DIAZ, Ahmet YILDIRIM, A. PEREZ-SESMA, R. CASTANEDA-SHEISSA, J. SANCHEZ-OREA, C. HOYOS-REYES
Applied Mathematics and Computation, SCI Expanded İndekslerine Giren Dergi, Uluslararası, Wos, 2013, cilt 219, ss 6707-6718
DOI: 10.1016/j.amc.2013.01.017
Özet
In this paper we study a generalization of the Johann Bernoulli's solution of the brachistocrone problem. We will see that his method can be quickly extended in such a way that it can be used to solve other problems in a similar way using just elementary calculus methods. In addition, we will show that it is not necessary to know Euler's formalism for the calculus of variations, making it a handy and useful method for engineering applications. The provided examples will illustrate that this technique is equivalent to Euler's equation of the calculus of variations; for the particular case where one of the variables do not appear explicitly. (C) 2013 Elsevier Inc. All rights reserved.