  We present a kinematic study of a thousand of dwarf satellites of MW/M31-like
hosts from the IllustrisTNG50 simulation. Internal kinematics were derived for
all the snapshots to obtain a historical record of their rotation velocity in
the plane of the sky ($|V_T|$) and the amplitude of their velocity gradients
along the line of sight ($A_{\rm grad}^{v_z}$) measured from the host. For the
majority of the satellites we initially detected rotation in the plane of the
sky (65%) or velocity gradients (80%), and this was progressively reduced to
45% and 68% at $z = 0$ respectively. We find that the evolution of the rotation
in the plane of the sky and the velocity gradients differs according to type of
dwarfs, which could be explained in terms of their different masses and orbital
histories. We observe that interaction with the host has an impact on the
evolution of the internal kinematics of the satellites. The rotation signal of
the satellites is progressively reduced during pericentric passages, the first
pericentre being especially disruptive for the initial kinematics. We observe
temporary increases in $A_{\rm grad}^{v_z}$ during pericentric passage caused
by tidal interaction with the host, $A_{\rm grad}^{v_z}$ increasing as the
satellites approach their pericentre and dropping as they move away. In
summary, we conclude that the presence of detectable rotation in dwarf
satellites is not uncommon, and that the evolution of their internal kinematics
is clearly affected by their interaction with the host.
