  Given a five dimensional space endowed with a Cartan distribution, the
abnormal geodesics form another five dimensional space with a cone structure.
Then it is shown, if the cone structure is regarded as a control system, then,
the space of abnormal geodesics of the cone structure is naturally identified
with the original space. In this paper, we provide an exposition on the duality
by abnormal geodesics in a wider framework, namely, in terms of quotients of
control systems and sub-Riemannian pseudo-product structures. Also we consider
the controllability of cone structures and describe the constrained Hamiltonian
equations on normal and abnormal geodesics.
