Abstract: Nonlinear self-spinning stability criteria of liquid-filled satellite with fotir-flexible-appendages are investigated with the Energy-Casimir method.The stability condi-tions take into account the vorticity of the liquid,the vibration of the flexible appendages,rota-tions of the rigid satellite,the coupling of liquid-elasticity-rigid,and centrifugal and coriolis forces.These results which are the extension of Rumjantsev's and Marsden's are obtained for the first time.

Key words: liquid-filled satellite, flexible appendages, Energy-Casimir method