Geodesic
Solution of a problem of S. Ulam on optimal matching of segments
Izvestiya. Mathematics, Tome 10 (1976) no. 3, pp. 639-651 Cet article a éte moissonné depuis la source Math-Net.Ru

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Using a maximum principle a solution is found of Ulam's problem of determining a continuous motion of a unit segment from the position $AB$ to $A'B'$ under which the total path traversed by the ends of this segment is as small as possible. Bibliography: 3 titles. 
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A. Ya. Dubovitskii. Solution of a problem of S. Ulam on optimal matching of segments. Izvestiya. Mathematics, Tome 10 (1976) no. 3, pp. 639-651. http://geodesic.mathdoc.fr/item/IM2_1976_10_3_a8/

[1] Ulam S., Nereshennye matematicheskie zadachi, Nauka, M., 1964 | Zbl

[2] Dubovitskii A. Ya., Integralnyi printsip maksimuma v obschei zadache optimalnogo upravleniya, dep. v VINITI, No 2 639-74 ot 10 oktyabrya 1974

[3] Dubovitskii A. Ya., Milyutin A. A., “Zadachi na ekstremum pri nalichii ogranichenii”, Zh. vychisl. matem. i matem. fiz., 5:3 (1965), 395–453 | Zbl