  While orbital analysis studies were so far mainly focused on the Galactic
halo, it is possible now to do these studies in the heavily obscured region
close to the Galactic Centre. We aim to do a detailed orbital analysis of stars
located in the nuclear stellar disc (NSD) of the Milky Way allowing us to trace
the dynamical history of this structure. We integrated orbits of the observed
stars in a non-axisymmetric potential. We used a Fourier transform to estimate
the orbital frequencies. We compared two orbital classifications, one made by
eye and the other with an algorithm, in order to identify the main orbital
families. We also compared the Lyapunov and the frequency drift techniques to
estimate the chaoticity of the orbits. We identified several orbital families
as chaotic, $z$-tube, $x$-tube, banana, fish, saucer, pretzel, 5:4, and 5:6
orbits. As expected for stars located in a NSD, the large majority of orbits
are identified as $z$-tubes (or as a sub-family of $z$-tubes). Since the latter
are parented by $x_{2}$ orbits, this result supports the contribution of the
bar (in which $x_{2}$ orbits are dominant in the inner region) in the formation
of the NSD. Moreover, most of the chaotic orbits are found to be contaminants
from the bar or bulge which would confirm the predicted contamination from the
most recent NSD models. Based on a detailed orbital analysis, we were able to
classify orbits into various families, most of which are parented by
$x_{2}$-type orbits, which are dominant in the inner part of the bar.
