高速公路的进出弧线:它们在变分法中的精确计算

IF 0.5 4区数学 Q3 MATHEMATICS

Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-09-12 DOI:10.4153/s000843952300070x

L. Bayón, P. Fortuny Ayuso, J.M. Grau, M.M. Ruiz

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引用次数: 0

摘要

摘要利用与欧拉方程相关的向量场相空间，以及初始/最终和/或横向条件，解决了一元情况下自主变分问题中高速公路入口弧和出弧的计算问题。结果取决于这样一种认识，即极值是已知函数的轮廓，而横截条件(一般)是一条曲线。给出了一种近似算法，并给出了一个算例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Entry and leaving arcs of turnpikes: their exact computation in the calculus of variations

Abstract We settle the question of how to compute the entry and leaving arcs for turnpikes in autonomous variational problems, in the one-dimensional case using the phase space of the vector field associated with the Euler equation, and the initial/final and/or the transversality condition. The results hinge on the realization that extremals are the contours of a well-known function and that the transversality condition is (generically) a curve. An approximation algorithm is presented, and an example is included for completeness.

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来源期刊

Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The Canadian Mathematical Bulletin was established in 1958 to publish original, high-quality research papers in all branches of mathematics and to accommodate the growing demand for shorter research papers. The Bulletin is a companion publication to the Canadian Journal of Mathematics that publishes longer papers. New research papers are published continuously online and collated into print issues four times each year. To be submitted to the Bulletin, papers should be at most 18 pages long and may be written in English or in French. Longer papers should be submitted to the Canadian Journal of Mathematics. Fondé en 1958, le Bulletin canadien de mathématiques (BCM) publie des articles d’avant-garde et de grande qualité dans toutes les branches des mathématiques, de même que pour répondre à la demande croissante d’articles scientifiques plus brefs. Le BCM se veut une publication complémentaire au Journal canadien de mathématiques, qui publie de longs articles. En ligne, il propose constamment de nouveaux articles de recherche, puis les réunit dans des numéros imprimés quatre fois par année. Les textes présentés au BCM doivent compter au plus 18 pages et être rédigés en anglais ou en français. C’est le Journal canadien de mathématiques qui reçoit les articles plus longs.