Stability of Relative Equilibria.
Part I: The Reduced Energy-Momentum Method

Simo, J. C., D. Lewis, and J. E. Marsden

Arch. Rational Mech. Anal., 115, 15-59

Abstract:

"Our main result is an explicit and readily implementable criterion for rigorous nonlinear stability of relative equilibria which is formulated exclusively in terms configuration variables."