Stability of Nonclassical Relative Equilibria of a Rigid Body in a J2 Gravity Field

The gravitationally coupled orbit-attitude dynamics of a rigid body in a J(2) gravity field is a generalization of the traditional point-mass J(2) problem to take into account the gravitational orbit-attitude coupling of the considered body. Linear and nonlinear stability of nonclassical relative equilibria in the coupled orbit-attitude dynamics are studied with geometric mechanics in the present paper. Conditions of stability are obtained through the linear system matrix and projected Hessian matrix by using the energy-Casimir method. Linear and nonlinear stability regions are plotted in a wide range of system parameters. It is found that the stability regions are similar to those of classical relative equilibria while, at the same time, some differences do exist. For example, in some cases, the linear stability region contains not only the two regions that are analogues of the Lagrange region and DeBra-Delp region, but also a small irregular region in the third quadrant. Same as the case of classical relative equilibria, the nonlinear stability region is the subset of the linear stability region in the first quadrant, which is the analogue of the Lagrange region. (C) 2016 American Society of Civil Engineers.