On the stability of the Lagrangian homographic solutions in a curved three-body problem on \(\mathbb{S}^2\). (English) Zbl 1263.70010
Summary: The problem of three bodies with equal masses in \(\mathbb{S}^2\) is known to have Lagrangian homographic orbits. We study the linear stability and also a “practical” (or effective) stability of these orbits on the unit sphere.
MSC:
| 70F07 | Three-body problems |
| 70H12 | Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics |
| 34D08 | Characteristic and Lyapunov exponents of ordinary differential equations |
| 37J25 | Stability problems for finite-dimensional Hamiltonian and Lagrangian systems |
