Stability of the rotating ellipsoidal D0-brane system

In this note we prove the complete stability of the classical fluctuation modes of the rotating ellipsoidal membrane. The analysis is carried out in the full SU(N) setting, with the conclusion that the fluctuation matrix has only positive eigenvalues. This proves that the solution will remain close to the original one for all time, under arbitrary infinitesimal perturbations of the gauge fields.