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arXiv · 2301.09886

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

L. Bayón·P. Fortuny Ayuso·J. M. Grau·M. M Ruiz
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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 to 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 that the transversality condition is (generically) a curve. An approximation algorithm is presented and an example included for completeness.

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L. Bayón, P. Fortuny Ayuso, J. M. Grau, M. M Ruiz. 2023-01-24. Entry and leaving arcs of turnpikes: their exact computation in the calculus of variations. https://arxiv.org/abs/2301.09886

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