Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.amc.2013.01.017 | Applied Mathematics and Computation |
Keywords | Field | DocType |
engineering application,particular case,brachistocrone problem,johann bernoulli,elementary calculus method,useful method,calculus of variations,integral,brachistochrone,differential equation | Mathematical analysis,Fluent calculus,Euler's formula,Brachistochrone curve,Mathematical optimization,Multivariable calculus,Algebra,Legendre–Clebsch condition,Calculus of variations,Time-scale calculus,Quantum stochastic calculus,Calculus,Mathematics | Journal |
Volume | Issue | ISSN |
219 | 12 | 0096-3003 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
8 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Uriel Filobello-Niño | 1 | 13 | 3.56 |
| H. Vazquez-Leal | 2 | 7 | 1.41 |
| D. Pereyra-Diaz | 3 | 0 | 0.34 |
| A. Yildirim | 4 | 33 | 4.95 |
| A. Perez-Sesma | 5 | 0 | 0.68 |
| Roberto Castañeda-Sheissa | 6 | 13 | 2.47 |
| Jesus Sanchez-Orea | 7 | 3 | 1.06 |
| C. Hoyos-Reyes | 8 | 0 | 0.34 |