In hierarchical structure formation, the content of a galaxy is determined both by its in-situ processes and by material added via accretions. Globular clusters in particular represent a window for the study of the different merger events that a galaxy underwent. Establishing the correct classification of in-situ and accreted tracers, and distinguishing the various different progenitors that contributed to the accreted population are important tools to deepen our understanding of galactic formation and evolution. Our aim is to refine our knowledge of the assembly history of the Milky Way by studying the dynamics of its globular cluster population and establishing an updated classification among in-situ objects and the different merger events identified. We used a custom built orbit integrator to derive precise orbital parameters, integrals of motions and adiabatic invariants for the globular cluster sample studied. By properly accounting for the rotating bar, which transforms the underlying model in a time-varying potential, we proceeded to a complete dynamical characterisation of the globular clusters. We present a new catalogue of clear associations between globular clusters and structures (both in-situ and accreted) in the Milky Way, and a full table of derived parameters. By using all dynamical information available, we were able to attribute previously unassociated or misclassified globular clusters to the different progenitors, including those responsible for the Aleph, Antaeus, Cetus, Elqui, and Typhon merger events. By using a custom built orbit integrator and properly accounting for the time-varying nature of the Milky Way potential, we have shown the depth of information that can be extracted from a purely dynamical analysis of the globular clusters of our Galaxy. By merging our dynamical analysis with complementary chronochemical studies, we will be able to uncover the remaining secrets of the accretion history of the Milky Way.