We present an analysis of the kinematics of 14 satellites of the Milky Way (MW). We use proper motions (PMs) from the $Gaia$ Early Data Release 3 (EDR3) and line-of-sight velocities ($v_{mathrm{los}}$) available in the literature to derive the systemic 3D motion of these systems. For six of them, namely the Carina, Draco, Fornax, Sculptor, Sextans, and Ursa Minor dwarf spheroidal galaxies (dSph), we study the internal kinematics projecting the stellar PMs into radial, $V_R$ (expansion/contraction), and tangential, $V_T$ (rotation), velocity components with respect to the centre of mass. We find significant rotation in the Carina ($|V_T| = 9.6 pm 4.5 {rm{km s^{-1}}}>$), Fornax ($|V_T| = 2.8 pm 1.3 {rm{km s^{-1}}}>$), and Sculptor ($|V_T| = 3.0 pm 1.0 {rm{km s^{-1}}}>$) dSphs. Besides the Sagittarius dSph, these are the first measurements of internal rotation in the plane of the sky in the MWs classical dSphs. All galaxies except Carina show $|V_T| / sigma_v < 1$. We find that slower rotators tend to show, on average, larger sky-projected ellipticity (as expected for a sample with random viewing angles) and are located at smaller Galactocentric distances (as expected for tidal stirring scenarios in which rotation is transformed into random motions as satellites sink into the parent halo). However, these trends are small and not statistically significant, indicating that rotation has not played a dominant role in shaping the 3D structure of these galaxies. Either tidal stirring had a weak impact on the evolution of these systems or it perturbed them with similar efficiency regardless of their current Galactocentric distance.
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