Abstract
The minimizing problem for the length of trajectories with respect to a submetric on a distribution is considered.
Quadratic sufficient conditions for the strong minimality of abnormal trajectories of arbitrary length are obtained.
The results hold for distributions of arbitrary dimensions and for a broad class of submetrics, including those
of sub-Riemannian and sub-Finsler metrics.

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ERRATUM (incorrect translation)
The first two sentences of the second paragraph on p. 369 should read:

A point is said to provide a {\it Pontryagin minimum} if, for any $N$, it is a point of local minimum
with respect to the norm $\|w\|_1$ on the part of the admissible set defined by the additional
condition $\|w\|_\infty\leq N$. This type of minimum is intermediate between the classical
weak and strong minima.

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