For geodesically accessible affine connection control systems, a quotient mechanical control system exists if and only if there is an involutive distribution on the configuration manifold that is invariant under the connection, the curvature, and the control vector fields.
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Quotients of affine connection control systems
For geodesically accessible affine connection control systems, a quotient mechanical control system exists if and only if there is an involutive distribution on the configuration manifold that is invariant under the connection, the curvature, and the control vector fields.