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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Note on a Noetherian conservation law and its corresponding general class of nonlinear second-order ordinary differential equations

Texto completo
Autor(es):
Casetta, Leonardo
Número total de Autores: 1
Tipo de documento: Artigo Científico
Fonte: ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK; v. 97, n. 2, p. 240-246, FEB 2017.
Citações Web of Science: 0
Resumo

By virtue of their fundamental nature and intrinsic elegance, there has long been a great interest in searching for the conservation laws of the problem at hand. In such field of research, the famous Noether's theorem has been recognized as a highlight. The objective of our note is to provide the reader with an original contribution to the study of Noetherian conservation laws. Namely, we aim at connecting a general class of nonlinear second-order ordinary differential equations with a Noetherian conservation law. Our analysis will be considered within the known structure of Noether's theorem. An aspect to be here emphasized is that, particularly, we will use the following simplifying assumptions: the invariance condition holds absolutely, the transformation generators do not depend on the derivative of the generalized coordinate with respect to the independent variable. We will present our contribution via a theorem and a corollary. First, our theorem will establish a general condition to obtain Noetherian conservation law for a certain type of variational problem. Then, the corollary will demonstrate that such Noetherian conservation law is a first integral for a general class of nonlinear second-order ordinary differential equations. This class of differential equations means the Lagrange's equation directly resulting from that type of variational problem. Last, a case of the Emden-Fowler equation will be presented as a testing example. (C) 2016 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim (AU)

Processo FAPESP: 12/10848-4 - Estudos Avançados em mecânica de sistemas de massa variável
Beneficiário:Leonardo Casetta
Linha de fomento: Bolsas no Brasil - Pós-Doutorado