Dynamics of two planets in the 2/1 mean-motion resonance
The discovery of extra-solar planets has increased the of investigations considering the long-term stability of different planetary systems. The main reasons for this increasing of the attention to the problem is that some above-mentioned systems are actually in resonant orbital configurations. Concerning the stability of motion of such systems, three important properties are usually under consideration: 1. First-order mean-motion resonances; 2. High-order mean-motion resonances; 3. The secular locking of the line of planetary orbit apses. In spite of some recent developments, the dynamics of the resonant and near resonant configurations in the planetary systems is still poorly understood. Here, the authors consider the 2/1 planetary mean-motion resonance. A general averaged planar two-degree-of-freedom Hamiltonian model is applied. The main regimes of motion of the system are obtained for a large set of initial conditions by means of surfaces of section and spectral map techniques. The results of the study are summarized on a plane defined by two parameters of the problem.
averaged two-degree-of-freedom Hamiltonian model
scientific article; zbMATH DE number 2140053