We consider the problem of quantizing a Skyrmion which is allowed to vibrate,
rotate and isorotate. Previous approaches have neglected the interactions
between vibrations and zero modes (analogous to so-called Coriolis terms in the
molecular physics literature). A new formalism incorporating these interactions
is introduced, inspired by a principal bundle approach to deformable-body
dynamics. We quantize the B=4 and B=7 Skyrmions and compare the results to
observed nuclear properties of Helium-4 and the Lithium-7/Beryllium-7 isospin
doublet
