The problem of stability in the context of elliptical galaxies is completely different from the studies of stability described in Part III. For disks, there are several specific morphological properties, in particular, spiral structures, bars, warps, and corrugations, that we may match in terms of appropriate modes over more symmetric equilibrium configurations. In the case of elliptical galaxies, there are no outstanding morphological features to be addressed in a similar manner. Some features do exist, for example, isophotal twisting, shells, and peculiar kinematics, that might in principle be considered, but their three-dimensional (3D) spatial structure is not known, and it is not clear whether their origin can be traced to simple low-amplitude regular patterns. Linear stability analyses also would be of little use for addressing one obvious question related to the departures from spherical symmetry: What intrinsic shapes are realized? In fact, natural modes to be considered (and in some cases found to be unstable) are those with l= 2, but they are a degenerate class that includes oblate, prolate, and triaxial perturbations. Thus one general motivation at the basis of many modal analyses (see Chapter 9) is simply not present in the case of elliptical galaxies.

There remain two major physical reasons to carry out stability investigations. One is the need for a good knowledge of the intrinsic modes of a dynamical system as a prerequisite to the proper description of the driven problem (e.g., for the study of tidal interactions).