  We derive an effective Hamiltonian system describing the low energy dynamics
of circular magnetic skyrmions and antiskyrmions. Using scaling and symmetry
arguments we model (anti-)skyrmion dynamics through a finite set of coupled,
canonically conjugated, collective coordinates. The resulting theoretical
description is independent of both micromagnetic details as well as any
specificity in the ansatz of the skyrmion profile. Based on the Hamiltonian
structure we derive a general description for breathing dynamics of
(anti-)skyrmions in the limit of radius much larger than the domain wall width.
The effective energy landscape reveals two qualitatively different types of
breathing behavior. For small energy perturbations we reproduce the well-known
small breathing mode excitations, where the magnetic moments of the skyrmion
oscillate around their equilibrium solution. At higher energies we find a
breathing behavior where the in-plane angle of the skyrmion continuously
precesses, transforming N\'eel to Bloch skyrmions and vice versa. For a damped
system we observe the transition from the continuously rotating and breathing
skyrmion into the oscillatory one. We analyze the characteristic frequencies of
both breathing types, as well as their amplitudes and distinct energy
dissipation rates. For rotational (oscillatory) breathing modes we predict on
average a linear (exponential) decay in energy. We argue that this stark
difference in dissipative behavior should be observable in the frequency
spectrum of excited (anti-)skyrmions.
