Geodesic
The index of the second variation of a control system
Sbornik. Mathematics, Tome 41 (1982) no. 3, pp. 383-401 Cet article a éte moissonné depuis la source Math-Net.Ru

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The constancy of sign of the second variation of a nonlinear control system is investigated. Sufficient conditions for controllability of second order and also sufficient conditions for optimality with respect to fast action of the extremals of this system analogous to the Legendre–Jacobi conditions of the classical calculus of variation are obtained. Bibliography: 6 titles. 
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A. V. Sarychev. The index of the second variation of a control system. Sbornik. Mathematics, Tome 41 (1982) no. 3, pp. 383-401. http://geodesic.mathdoc.fr/item/SM_1982_41_3_a3/

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