For a control system on the sphere with two skew-symmetric matrices A and B, the nonzero bracket condition [A,B]≠0 guarantees controllability, and the paper constructs the steering trajectories explicitly.
Colque.Controlabilidad de sistemas bilineales inducidos en la esferaS 2,Tesis de Maestria, Carrera de Matem´ atica (2025), in preparation
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Controllability of induced bilinear systems on the sphere
For a control system on the sphere with two skew-symmetric matrices A and B, the nonzero bracket condition [A,B]≠0 guarantees controllability, and the paper constructs the steering trajectories explicitly.