Skip Navigation

IMA Journal of Mathematical Control and Information 1988 5(2):125-145; doi:10.1093/imamci/5.2.125
© 1988 by Institute of Mathematics and its Applications
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by ROSENBLUETH, J. F.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Systems with Time Delay in the Calculus of Variations: A Variational Approach

JAVIER F. ROSENBLUETH

Centro de Investigación en Matemáticas, A. C. Apartado Postal 402, Guanajuato, Gto., 36000, Mexico

In this paper, we deal with the fixed-endpoint problem in the calculus of variations involving a delay in the phase coordinates. Necessary conditions in the form of a maximum principle are well known and, hence, conditions equivalent to those of Euler, Legendre, and Weierstrass. However, no results seem to exist for sufficiency, or for a corresponding Jacobi condition. We derive necessary and sufficient conditions in terms of the first and second variations, extending the clssical results for the delay-free case. This is obtained directly, that is, without referring to concepts such as conjugate points, fields of extremals, Riccati equations, or the Hamilton-Jacobi partial differential equation. The first-order condtion is then characterized in terms of the Euler equation, together with smoothness properties of solutions. Several examples illustrate the usefulness of the conditions obtained.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.