高速公路的进出弧线:它们在变分法中的精确计算

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。

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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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