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The classical problem of attitude stability in a central gravity field isgeneralized 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 Hamiltonianstructure of the problem is derived. The Poisson tensor, Casimir functions andequations of motion are obtained in a differential geometric method. Theequilibrium of the equations of motion, i.e. the equilibrium attitude of thespacecraft, is determined from a global point of view. Nonlinear stabilityconditions of the equilibrium attitude are obtained with the energy-Casimirmethod. The nonlinear attitude stability is then investigated versus threeparameters of the asteroid, including the ratio of the mean radius to thestationary orbital radius, the harmonic coefficients C20 and C22. It is foundthat when the spacecraft is located on the intermediate-moment principal axisof the asteroid, the nonlinear stability domain can be totally different fromthe classical Lagrange region on a circular orbit in a central gravity field.

Nonlinear attitude stability of a spacecraft on a stationary orbit around an asteroid subjected to gravity gradient torque