# A.A. Agrachev, A.V. Sarychev, On reduction of a smooth system linear in the control

Title: On reduction of a smooth system linear in the control
Authors: A.A. Agrachev, A.V. Sarychev
Journal title: Mathematics of the USSR-Sbornik
Year: 1987
Issue: 1
Volume: 58
Pages: 15–30
Citation:

A. A. Agrachev, A. V. Sarychev, “On reduction of a smooth system linear in the control”, Mathematics of the USSR-Sbornik, 1987, 58:1, 15–30

Abstract:

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.