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On reduction of a smooth system linear in the control. (English. Russian original) Zbl 0678.49034
Math. USSR, Sb. 58, 15-30 (1987); translation from Mat. Sb., Nov. Ser. 130(172), No. 1, 18-34 (1986).
Summary: 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.

MSC:
93B03 Attainable sets, reachability
49K15 Optimality conditions for problems involving ordinary differential equations
37C10 Dynamics induced by flows and semiflows
93B05 Controllability
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