研究轨道共振的一种分析平均模型

AN ANALYTICAL AVERAGE MODEL OF STUDIES ON ORBITAL RESONANCE

本文考察了目前研究轨道共振几种模型的特点,提出了一种分析平均模型,对于研究轨道共振的特征和演化均有方便之处.

For a long time, from the aspect of gravitation, there are two methematical models in studing orbital resonance: practical and averaged models. It isn't convenient to use the practical model, because being devoid of any simplications in discussed dynamic systems, and fast variations are contained in the perturbation function. For this reason, most of the authors use the averaged model, in which the perturbation function is averaged and the fast variations are cancelled. The averaged model is classified by numerical averaged and ideal resonant models, called the Schubart's and Garfincal's models, respectively. Based on Schubart's model, the perturbation function of the system is expanded trigonometrically in the mean anomaly of the perturbed and perturbing bodies, The secular and resonant terms are taken in the meaning of first order. Therefore we obtain H_L, Hamiltonian of the resonant system, as follows: H_L=1/2a+R_c+R_l+R_r H_L is called the analytical averaged model. H_L is discussed in detail and compared with the Schubart's model and practical model, respectively, in this paper. We can see that it is significance to establish H_L and convenient for researching the characteristics and evolution of orbital resonance.