Geodesic
On reduction of a smooth system linear in the control
Sbornik. Mathematics, Tome 58 (1987) no. 1, pp. 15-30 
A. A. Agrachev; A. V. Sarychev. On reduction of a smooth system linear in the control. Sbornik. Mathematics, Tome 58 (1987) no. 1, pp. 15-30. http://geodesic.mathdoc.fr/item/SM_1987_58_1_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A method is presented for reducing a smooth system linear in the control on an $n$-dimensional manifold $M$ to a nonlinear system on an $(n-1)$-dimensional manifold. This reduction is used to obtain sufficient conditions for a high order of local controllability of the system, and the problem of a time-optimal control of the angular momentum of a rotating rigid body is investigated. Bibliography: 7 titles.

[1] Agrachev A. A., Gamkrelidze R. V., “Eksponentsialnoe predstavlenie potokov i khronologicheskoe ischislenie”, Matem. sb., 107(149) (1978), 476–532 | MR

[2] Sussmann H. J., Jurdjevic V., “Controllability of nonlinear systems”, J. Diff. Equat., 12 (1972), 95–116 | DOI | MR | Zbl

[3] Gamkrelidze R. V., Osnovy optimalnogo upravleniya, Izd-vo Tbilisskogo un-ta, Tbilisi, 1977 | MR | Zbl

[4] Sussmann H. J., “Lie brackets, real analiticity and geometric control”, Differential geometric control theory. Proc. of the conf. held at Michigan Technol. Univ. (June 28–July 2, 1982. Birkhauser), Boston–Basel–Stuttgart, 1983, 1–116 | MR | Zbl

[5] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1974 | MR

[6] Agrachev A. A., Sarychev A. V., “The control of rotation for asymmetric rigid body”, Probl. of Control and Information Theory, 12(5) (1983), 335–347 | MR | Zbl

[7] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR | Zbl