关于轨道共振的演化性态

ON THE EVOLUTION OF ORBITAL RESONANCE

轨道共振的特征可从相应的平均化后的理想共振模型中获得,但在受摄情况下,当t—1/ε,甚至t》1/ε时(ε是摄动小参数),共振运动的性态又将如何这是至关重要的问题。当然,该问题与结构稳定性有关,但有它自身的特殊性,即只需考查共振态能否保持,本文将着重讨论小行星的轨道共振,并通过对几种主要通约比(3/1,2/1,3/2)的情况,进行近似分析和数值探索来阐明共振态的演化以及各种摄动因素的影响,发现了不同通约比对应的共振态演化间的某些差别.

The characteristics of orbital resonance can be revealed by the model of the corresponding ideal resonance which is obtained with the averasing method. How the resonant motion evolves under the action of perturbation, when t～1/ε, even t>>1/ε, where ε is a small perturbing parameter This is an important problem for the study of orbital resonance. The problem is related to the structural stability, but it has its own speciality. Namely, one should only investigate whether the resonant state can be retained. In this paper, we study mainly the orbital resonance of asteroids and try to clarify the evolution of the resonant state and the influence of the perturbing factors by both numerical investigation and the retical analysis for some commensurate rations, we have found preliminarly some differences among them.