Filobello-Nino U, Vazquez-Leal H, Huerta-Chua J, Callejas-Molina R A, Sandoval-Hernandez M A
Facultad de Instrumentación Electrónica, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, Xalapa, Veracruz, 91000, Mexico.
Consejo Veracruzano de Investigación Científica y Desarrollo Tecnológico (COVEICYDET), Av. Rafael Murillo Vidal No. 1735, Cuauhtemoc, Xalapa, Veracruz, 91069, Mexico.
Heliyon. 2020 Apr 1;6(4):e03703. doi: 10.1016/j.heliyon.2020.e03703. eCollection 2020 Apr.
The aim of this article is to show the way to get both, exact and analytical approximate solutions for certain variational problems with moving boundaries but without resorting to Euler formalism at all, for which we propose two methods: the Moving Boundary Conditions Without Employing Transversality Conditions (MWTC) and the Moving Boundary Condition Employing Transversality Conditions (METC). It is worthwhile to mention that the first of them avoids the concept of transversality condition, which is basic for this kind of problems, from the point of view of the known Euler formalism. While it is true that the second method will utilize the above mentioned conditions, it will do through a systematic elementary procedure, easy to apply and recall; in addition, it will be seen that the Generalized Bernoulli Method (GBM) will turn out to be a fundamental tool in order to achieve these objectives.
本文的目的是展示一种方法，即对于某些具有移动边界的变分问题，无需借助欧拉形式主义，就能获得精确解和解析近似解。为此，我们提出两种方法：不采用横截性条件的移动边界条件法（MWTC）和采用横截性条件的移动边界条件法（METC）。值得一提的是，从已知的欧拉形式主义角度来看，第一种方法避免了横截性条件这一此类问题的基本概念。虽然第二种方法确实会利用上述条件，但它将通过一个系统的基本程序来实现，该程序易于应用和记忆；此外，为了实现这些目标，广义伯努利方法（GBM）将被证明是一个基本工具。
