MOTION STABILITY OF A DEFORMABLE BODY IN AN IDEAL FLUID WITH APPLICATIONS TO THE N SPHERES PROBLEM

The Liapunov stability problem of the translation or spiraling motion of an arbitrary deformable body (the deformation of which is governed by the corresponding Hamiltonian) is treated here using the modified E nergy-Casimir approach. The appropriate stability criteria are derived . It is shown that some unstable translational motions can be stabiliz ed by a deformational or rotational motion. This formalism is further applied to the stability problem related to the motion of N (generally unequal) rigid spheres embedded in a potential flow field. The assemb ly of N-spheres is treated as an entire N-connected single deformable body. The Liapunov stability of the motion of two spheres in the direc tion orthogonal to their Lines of centers and that of three spheres in the direction orthogonal to their plane of centers, is demonstrated a nd proven as a special case. Some existing conditions of clustering fo r a bubble cloud are also rederived and extended. (C) 1998 American In stitute of Physics.