Morse index and stability of elliptic Lagrangian solutions in the planar three-body problem |
| |
Authors: | Xijun Hu Shanzhong Sun |
| |
Institution: | a Department of Mathematics, Shandong University, Jinan, Shandong, 250100, People's Republic of China b Department of Mathematics, Capital Normal University, Beijing, 100048, People's Republic of China |
| |
Abstract: | We illustrate a new way to study the stability problem in celestial mechanics. In this paper, using the variational nature of elliptic Lagrangian solutions in the planar three-body problem, we study the relation between Morse index and its stability via Maslov-type index theory of periodic solutions of Hamiltonian system. For elliptic Lagrangian solutions we get an estimate of the algebraic multiplicity of unit eigenvalues of its monodromy matrix in terms of the Morse index, which is the key to understand the stability problem. As a special case, we provide a criterion to spectral stability of relative equilibrium. |
| |
Keywords: | Planar three-body problem Lagrangian solution Linear stability Morse index Maslov-type index |
本文献已被 ScienceDirect 等数据库收录! |
|