A global version of the Koon-Marsden Jacobiator formula

In this paper we study the Jacobiator (the cyclic sum that vanishes when the Jacobi identity holds) of the almost Poisson brackets describing nonholonomic systems. We revisit the local formula for the Jacobiator established by Koon and Marsden in \cite{MarsdenKoon} using suitable local coordinates and explain how it is related to the global formula obtained in \cite{paula}, based on the choice of a complement to the constraint distribution. We use an example to illustrate the benefits of the coordinate-free viewpoint.