A LYAPUNOV FUNCTIONAL FOR STABILITY OF IDEAL MAGNETOHYDRODYNAMIC SYSTEMS IN ARBITRARY MOTION

The stability properties of an ideal magnetohydrodynamic (MHD) fluid ( compressible) in an arbitrary state of motion is explored. A stability condition is formulated in general terms based on the concept of a Ly apunov functional for the system which can be taken to be the Hamilton ian. Special consideration is given to stationary systems where the fl uid is bounded by a surface on which the normal component of the fluid velocity is zero. For this case a necessary and sufficient condition for stability in terms of an energy principle is formulated. This can be considered to be a generalization of the classic MHD energy princip le. A comparison to normal mode solutions is made. Systems being subje cted to forced oscillations around a static equilibrium that may be un stable are of prime interest for dynamic stabilization problems. The p resent theory also includes results relevant to this type of system, a lthough no details of such problems are presented. The emphasis is on general theory, however, one example of an ordinary fluid which is rot ating is discussed in order to get a better understanding of the theor etical results. (C) 1997 American Institute of Physics.