We analyze controllability and observability conditions for second order descriptor systems and show how the classical conditions for first order systems can be generalized to this case. We show that performing a classical transformation to first order form may destroy some controllability and observability properties. As an example, we demonstrate that the loss of impulse controllability in constrained multibody systems is due to the representation as a first order system. To avoid this problem, we will derive a canonical form and new first order formulations that do not destroy the controllability and observability properties.