Abstract This paper studies the orbital dynamics of the potential of asteroid 22 Kalliope using observational data of the irregular shape. The zero-velocity surface are calculated and showed with different Jacobian values. All five equilibrium points are found, four of them are outside and unstable, and the other one is inside and linearly stable. The movement and bifurcations of equilibrium points during the variety of rotation speed and density of the body are investigated. The Hopf bifurcations occurs during the variety of rotational speed from ω=1.0ω0 to 0.5ω0, and the Saddle-Node bifurcation occurs during the variety of rotational speed from ω=1.0ω0 to 2.0ω0. Both unstable and stable resonant periodic orbits around Kalliope are coexisting. The perturbation of an unstable periodic orbit shows that the gravitational field of Kalliope is strongly perturbed.

中文翻译：

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小行星 22 Kalliope 动力环境中的平衡和轨道

摘要 本文利用不规则形状的观测资料研究了小行星22 Kalliope 的轨道动力学。计算零速度表面并用不同的雅可比值显示。找到所有五个平衡点，其中四个在外部且不稳定，另一个在内部且线性稳定。研究了物体旋转速度和密度变化时平衡点的运动和分岔。Hopf 分岔发生在转速从 ω=1.0ω0 到 0.5ω0 的变化过程中，鞍节点分叉发生在转速从 ω=1.0ω0 到 2.0ω0 的变化过程中。围绕 Kalliope 的不稳定和稳定的共振周期轨道是共存的。