  The inertial effects of magnetic solitons play a crucial role in their
dynamics and stability. Yet governing their inertial effects is a challenge for
their use in real devices. Here, we show how to control the inertial effects of
magnetic droplet solitons. Magnetic droplets are strongly nonlinear and
localized autosolitons than can form in current-driven nanocontacts. Droplets
can be considered as dynamical particles with an effective mass. We show that
the dynamical droplet bears a second excitation under its own inertia. These
excitations comprise a chiral profile, and appear when the droplet resists the
force induced by the Oersted field of the current injected into the
nanocontact. We reveal the role of the spin torque on the excitation of these
chiral modes and we show how to control these modes using the current and the
field.
