The rotational motion of a rigid dynamical system including a three dimensional elastic part about a fixed point is studied. The system is under the action of a general gravitational field. The stability anlysis is carried out by expanding the displacement of the deformable part in terms of orthonormalized functions with the independent coefficients. Results are obtained easily based on Routh's equation and Andoyer variables. The system is found to be stable provided that the dissipation energy is minimum corresponds to the case of axially symmetric deformation. On the other hand, the system is unstable, when the angular momentum vector is parallel to the equatorial plane, (C) 1998 Elsevier Science Ltd. [References: 11]
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