  Sub-Riemannian cubics are a generalisation of Riemannian cubics to a
sub-Riemannian manifold. Cubics are curves which minimise the integral of the
norm squared of the covariant acceleration. Sub-Riemannian cubics are cubics
which are restricted to move in a horizontal subspace of the tangent space.
When the sub-Riemannian manifold is also a Lie group, sub-Riemannian cubics
correspond to what we call a sub-Riemannian Lie quadratic in the Lie algebra.
The present article studies sub-Riemannian Lie quadratics in the case of
$\mathfrak{su}(2)$, focusing on the long term dynamics.
