A practical proposal to obtain solutions of certain variational problems avoiding Euler formalism
U. Filobello-Nino,
H. Vazquez-Leal,
J. Huerta-Chua,
R.A. Callejas-Molina,
M.A. Sandoval-Hernandez
Affiliations
U. Filobello-Nino
Facultad de Instrumentación Electrónica, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, Xalapa, Veracruz, 91000, Mexico
H. Vazquez-Leal
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; Corresponding author.
J. Huerta-Chua
Instituto Tecnológico Superior de Poza Rica, Tecnológico Nacional de México, Luis Donaldo Colosio Murrieta S/N, Arroyo del Maíz, C.P. 93230 Poza Rica, Veracruz, Mexico
R.A. Callejas-Molina
Instituto Tecnológico de Celaya, Tecnológico Nacional de México, Antonio García Cubas Pte. #600, Celaya, Guanajuato, Mexico
M.A. Sandoval-Hernandez
Escuela de Ingeniería, Universidad de Xalapa, Km 2, Carr. Xalapa-Veracruz 341, 91190 Xalapa, Veracruz, Mexico
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.
