  We consider dynamical axion phenomena in topological superconductors and
superfluids in three spatial dimensions in terms of the gravitoelectromagnetic
topological action, in which the axion field couples with mechanical rotation
under finite temperature gradient. The dynamical axion is induced by relative
phase fluctuations between topological and s-wave superconducting orders. We
show that an antisymmetric spin-orbit interaction which induces parity-mixing
of Cooper pairs enlarges the parameter region in which the dynamical axion
fluctuation appears as a low-energy excitation. We propose that the dynamical
axion increases the moment of inertia, and in the case of ac mechanical
rotation, i.e. a shaking motion with a finite frequency $\omega$, as $\omega$
approaches the dynamical axion fluctuation mass, the observation of this effect
becomes feasible.
