  Context. Recent observational data show that the Milky Way (MW) galaxy
contains about 170 globular clusters (GCs). A fraction of them is likely formed
in dwarf galaxies accreted onto the MW in the past, while the remaining of
clusters are formed in-situ. Therefore, different parameters, including orbits,
of the globular clusters is a valuable tool for studying the Milky Way
evolution. However, since the evolution of the 3D mass distribution of the MW
is poorly constrained, the orbits of the clusters are usually calculated in
static potentials.
  Aims. In this work, we study the evolution of the GCs in several external
potentials, where we aim to quantify the effects of the evolving galaxy
potential on the orbits of the GCs. Methods. For the orbits calculation we used
five MW-like potentials from IllustrisTNG-100 simulation. The orbits of 159 GCs
were integrated using a high-order N-body parallel dynamic code phi-GPU, with
initial conditions obtained from recent Gaia DR3 catalogues.
  Results. We provide a classification of the GCs orbits according to their 3D
shapes and association with different components of the MW (disk, halo, bulge).
We also found that the globular clusters in the external potentials have
roughly similar energy-angular momentum distributions at the present time.
However, both total energy and total angular momentum of the GCs are not
conserved due to time-varying nature of the potentials. In some extreme cases,
the total energy can change up to 40% (18 objects) over the last 5 Gyr of
evolution. We found that the in-situ formed GCs are less affected by the
evolution of the TNG potentials as compared to the clusters which are likely
formed ex-situ. Therefore, our results suggest that time-varying potentials
significantly affect the orbits of the GC, thus making it vital for
understanding the formation of the MW.
