Geodesic
A~second order optimality principle for a~time-optimal problem
Sbornik. Mathematics, Tome 29 (1976) no. 4, pp. 547-576

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In this paper, a general necessary optimality condition of second order is proved for a time-optimal problem. Necessary optimality conditions of second order are applied, in general, in studying singular optimal regimes which can not be found with the aid of the first-order necessary condition for optimality, i.e. with the aid of the Pontryagin maximum principle. Bibliography: 4 titles. 
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     title = {A~second order optimality principle for a~time-optimal problem},
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A. A. Agrachev; R. V. Gamkrelidze. A~second order optimality principle for a~time-optimal problem. Sbornik. Mathematics, Tome 29 (1976) no. 4, pp. 547-576. http://geodesic.mathdoc.fr/item/SM_1976_29_4_a6/