Scheeres D J
The University of Michigan, Ann Arbor, MI 48109-2140, USA.
Ann N Y Acad Sci. 2004 May;1017:81-94. doi: 10.1196/annals.1311.006.
The stability of relative equilibrium solutions for the interaction of two massive bodies is explored. We restrict ourselves to the interaction between an ellipsoid and a sphere, both with finite mass. The study of this problem has application to modeling the relative dynamics of binary asteroids, the motion of spacecraft about small bodies, and the dynamics of gravity gradient satellites. The relative equilibrium can be parameterized by a few constants, including the mass ratio of the two bodies, the shape of the ellipsoid, and the normalized distance between the two bodies. Planar stability is characterized over this range of parameter values. When restricted to motion in the symmetry plane, the dynamical problem can be reduced to a two-degrees of freedom Hamiltonian system, which allows for an efficient computation of stability characteristics of the relative equilibria. Future work will look at full stability of these relative equilibria.
研究了两个大质量物体相互作用时相对平衡解的稳定性。我们将研究范围限定为一个有限质量的椭球体与一个有限质量的球体之间的相互作用。对该问题的研究可应用于双星小行星相对动力学建模、航天器绕小天体的运动以及重力梯度卫星的动力学。相对平衡可以由几个常数参数化，包括两个物体的质量比、椭球体的形状以及两个物体之间的归一化距离。在此参数值范围内表征了平面稳定性。当限制在对称平面内运动时，动力学问题可简化为一个二自由度哈密顿系统，这使得能够高效计算相对平衡的稳定性特征。未来的工作将研究这些相对平衡的完全稳定性。
