Vertical lifts create linear control problems on tangent spaces, with fiberwise controllability equivalent to rank conditions, and for drift-plus-vertical systems, conditions via transported vector fields.
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Vertical Control Systems on Tangent Bundles and Fiberwise Controllability
Vertical lifts create linear control problems on tangent spaces, with fiberwise controllability equivalent to rank conditions, and for drift-plus-vertical systems, conditions via transported vector fields.