  The classical problem of attitude stability in a central gravity field is
generalized to that on a stationary orbit around a uniformly-rotating asteroid.
This generalized problem is studied in the framework of geometric mechanics.
Based on the natural symplectic structure, the non-canonical Hamiltonian
structure of the problem is derived. The Poisson tensor, Casimir functions and
equations of motion are obtained in a differential geometric method. The
equilibrium of the equations of motion, i.e. the equilibrium attitude of the
spacecraft, is determined from a global point of view. Nonlinear stability
conditions of the equilibrium attitude are obtained with the energy-Casimir
method. The nonlinear attitude stability is then investigated versus three
parameters of the asteroid, including the ratio of the mean radius to the
stationary orbital radius, the harmonic coefficients C20 and C22. It is found
that when the spacecraft is located on the intermediate-moment principal axis
of the asteroid, the nonlinear stability domain can be totally different from
the classical Lagrange region on a circular orbit in a central gravity field.
