A generalization of the Bernoulli's method applied to brachistochrone-like problems


FILOBELLO-NINO U., VAZQUEZ-LEAL H., PEREYRA-DIAZ D., YILDIRIM A. , PEREZ-SESMA A., CASTANEDA-SHEISSA R., ...Daha Fazla

APPLIED MATHEMATICS AND COMPUTATION, cilt.219, ss.6707-6718, 2013 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 219 Konu: 12
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1016/j.amc.2013.01.017
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Sayfa Sayıları: ss.6707-6718

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.