We present and discuss the 2D kinematic properties of the ionized gas ( H \alpha ) in a sample of 38 local ( ultra ) luminous infrared galaxies [ ( U ) LIRGs ] ( 31 LIRGs and 7 ULIRGs , 51 individual galaxies ) observed with VIMOS at the Very Large Telescope using optical integral field spectroscopy ( IFS ) . This sample covers well the less studied LIRG luminosity range and includes the morphological types corresponding to the different phases along the merging process ( i.e. , isolated disks , interacting systems , and mergers ) . The majority of the galaxies have two main kinematically distinct components . One component ( i.e. , narrow or systemic ) extends over the whole line-emitting region and is characterized by small to intermediate velocity dispersions ( i.e. , \sigma from 30 to 160 km s ^ { -1 } ) . The second component ( broad ) has in general a larger velocity dispersion ( up to 320 km s ^ { -1 } ) ; it is mainly found in the inner regions and is generally blueshifted with respect to the systemic component . The largest extensions and extreme kinematic properties of the broad component are observed in interacting and merging systems , and they are likely associated with nuclear outflows . The systemic component traces the overall velocity field showing a large variety of kinematic 2D structures , from very regular velocity patterns typical of pure rotating disks ( 29 % ) to kinematically perturbed disks ( 47 % ) and highly disrupted and complex velocity fields ( 24 % ) . Thus , most of the objects ( 76 % ) are dominated by rotation . We find that rotation is more relevant in LIRGs than in ULIRGs . There is a clear correlation between the different phases of the merging process and the mean kinematic properties inferred from the velocity maps . In particular , isolated disks , interacting galaxies , and merging systems define a sequence of increasing mean velocity dispersion , and decreasing velocity field amplitude , characterized by average dynamical ratios ( v _ { shear } ^ { * } / \sigma _ { mean } ) of 4.7 , 3.0 and 1.8 , respectively . We also find that the ratio between the nuclear ( \sigma _ { c } ) and the mean velocity dispersions ( \sigma _ { mean } ) vs . \sigma _ { mean } is an excellent discriminating plane between disks and interacting/merging systems : disks show a mean ratio a factor of 2 larger than those characterizing the other two classes . The LIRGs classified as isolated disks have similar velocity amplitudes but larger mean velocity dispersions ( 44 vs. 24 km s ^ { -1 } ) than local spirals , implying a larger turbulence and thicker disks . Interacting systems and mergers have values closer to those of low velocity dispersion ellipticals/lenticular galaxies ( E/SOs ) . The subclass of ( U ) LIRGs classified as mergers have kinematic properties similar to those shown by the Lyman break analogs ( LBAs ) , although the dynamical mass of LBAs is five times lower on average . Therefore , despite the difference in mass and dust content , the kinematics of these two local populations appears to have significant noncircular motions . These motions may be induced by the tidal forces , producing dynamically hot systems . The dynamical masses range from \sim 0.04 m _ { \star } to 1.4 m _ { \star } ( i.e. , m _ { \star } = 1.4 \times 10 ^ { 11 } M _ { \odot } ) , with ULIRGs ( M _ { dyn } \sim 0.5 \pm 0.2 m _ { \star } ) being more massive than LIRGs by , on average , a factor of about 2 . The mass ratio of individual pre-coalescence galaxies is < 2.5 for most of the systems , confirming that most ( U ) LIRG mergers involve sub-m _ { \star } galaxies of similar mass .