  We present dynamical measurements from the KMOS (K-band Multi-Object
Spectrograph) Deep Survey (KDS), which is comprised of 77 typical star-forming
galaxies at z $\simeq$ 3.5 in the mass range 9.0 < log(M$_{\star}$/M$_{\odot}$)
< 10.5. These measurements constrain the internal dynamics, the intrinsic
velocity dispersions ({\sigma}$_{int}$) and rotation velocities (V$_{C}$) of
galaxies in the high redshift Universe. The mean velocity dispersion of the
galaxies in our sample is {\sigma}$_{int}$ = $70.8^{+3.3}_{-3.1}$ km s$^{-1}$,
revealing that the increasing average {\sigma}$_{int}$ with increasing
redshift, reported for z $\lesssim2$, continues out to z $\simeq$ 3.5. Only 34
$\pm$ 8% of our galaxies are rotation-dominated (V$_{C}$/{\sigma}$_{int}$ > 1),
with the sample average V$_{C}$/{\sigma}$_{int}$ value much smaller than at
lower redshift. After carefully selecting comparable star-forming samples at
multiple epochs, we find that the rotation-dominated fraction evolves with
redshift with a z$^{-0.2}$ dependence. The rotation-dominated KDS galaxies show
no clear offset from the local rotation velocity-stellar mass (i.e.
V$_{C}$-M$_{\star}$) relation, although a smaller fraction of the galaxies are
on the relation due to the increase in the dispersion-dominated fraction. These
observations are consistent with a simple equilibrium model picture, in which
random motions are boosted in high redshift galaxies by a combination of the
increasing gas fractions, accretion efficiency, specific star-formation rate
and stellar feedback and which may provide significant pressure support against
gravity on the galactic disk scale.
