On motions with bursting characters for Lagrangian mechanical systems with a scalar control. II: A geodesic property of motions with bursting characters for Lagrangian systems (Q1195193)

Summary: This note is the continuation of a previous paper [see the authors, ibid., Mat. Appl. 2, No. 4, 339-343 (1991; Zbl 0784.70025)]. Here we show that for every choice of the sequence \(u_ a(\cdot),\Sigma_ a\)'s trajectory \(l_ a\) after the instant \(d+\eta_ a\) tends in a certain natural sense, as \(a\to \infty\), to a certain geodesic \(l\) of \(V_ d\), with origin at \((\overline{q},\overline{u})\). Incidentally \(l\) is independent of the choice of applied forces in a neighbourhood of \((\overline{q},\overline{u})\) arbitrarily prefixed.