Geodesic
The index of the second variation of a control system
Matematičeskij sbornik, Tome 155 (1980) no. 3, pp. 464-486.

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Keywords: second variation, conjugate point of an extremal time-optimal system, Morse index, Legendre condition 
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А.В. Сарычев. The index of the second variation of a control system. Matematičeskij sbornik, Tome 155 (1980) no. 3, pp. 464-486. http://geodesic.mathdoc.fr/item/MS_1980__155_3_a3/