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Taking all the magnon modes into account, we derive the skyrmion dynamics inresponse to a weak external drive. A skyrmion has rotational symmetry and themagnon modes can be characterized by an angular momentum. For a weak distortionof a skyrmion, only the magnon modes with an angular momentum $|m|=1$ governthe dynamics of skyrmion topological center. The skyrmion inertia is determinedby the magnon modes in the continuum spectrum. For a skyrmion driven by amagnetic field gradient or by a spin transfer torque generated by a current,the dynamical response is practically instantaneous. This justifies the rigidskyrmion approximation used in Thiele's collective coordinate approach. For askyrmion driven by a spin Hall torque, the torque couples to the skyrmionmotion through the magnons in the continuum and damping, therefore the skyrmiondynamics shows sizable inertia in this case. The trajectory of a skyrmion is anellipse for an ac drive of spin Hall torque.

Dynamics and inertia of a skyrmion in chiral magnets and interfaces: A linear response approach based on magnon excitations