  Filaments are ubiquitous in the interstellar medium (ISM), yet their
formation and evolution remains the topic of intense debate. In order to obtain
a more comprehensive view of the 3D morphology and evolution of the Musca
filament, we model the C$^{18}$O(2-1) emission along the filament crest with
several large-scale velocity field structures. This indicates that Musca is
well described by a 3D curved cylindrical filament with longitudinal mass
inflow to the center of the filament unless the filament is a transient
structure with a lifetime $\lesssim$~0.1 Myr. Gravitational longitudinal
collapse models of filaments appear unable to explain the observed velocity
field. To better understand these kinematics, we further analyze a map of the
C$^{18}$O(2-1) velocity field at the location of SOFIA HAWC+ dust polarization
observations that trace the magnetic field in the filament. This unveils an
organized magnetic field that is oriented roughly perpendicular to the filament
crest. Although the velocity field is also organized, it progressively changes
its orientation by more than 90$^{o}$ when laterally crossing the filament
crest and thus appears disconnected from the magnetic field in the filament.
This strong lateral change of the velocity field over the filament remains
unexplained and might be associated with important longitudinal motion in the
filament that can be associated to the large-scale kinematics along the
filament.
