  A Dalitz plot analysis of the $D_s^+ \to \pi^- \pi^+ \pi^+$ decay is
presented. The analysis is based on proton-proton collision data recorded by
the LHCb experiment at a centre-of-mass energy of $8$ TeV and corresponding to
an integrated luminosity of $1.5 fb^{-1}$. The resonant structure of the decay
is obtained using a quasi-model-independent partial-wave analysis, in which the
$\pi^+\pi^-$ S-wave amplitude is parameterised as a generic complex function
determined by a fit to the data. The S-wave component is found to be dominant,
followed by the contribution from spin-2 resonances and a small contribution
from spin-1 resonances. The latter includes the first observation of the $D_s^+
\to \omega(782) \pi^+$ channel in the $D_s^+ \to \pi^- \pi^+ \pi^+$ decay. The
resonant structures of the $D_s^+ \to \pi^- \pi^+ \pi^+$ and $D^+ \to \pi^-
\pi^+ \pi^+$ decays are compared, providing information about the mechanisms
for the hadron formation in these decays.
