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 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.