Abstract
In the Robe’s restricted three-body problem, we have considered the motion of the test particle which is moving inside the outermost layer of the heterogeneous body. This heterogeneous body has N layers with different densities and is filled with viscous fluid. The test particle which is taken as the third (or infinitesimal) body is moving under the influence of the heterogeneous body (primary) and point mass (secondary). We are motivated from Ansari,1 where the linear stability and other important properties of this specific model have been discussed. In this paper, we have extended their work and discussed here the nonlinear stability of the non-collinear stationary points L4 and L5. Therefore, using the Arnold–Moser theorem (Kolmogorov–Arnold–Moser theory), we have done our analysis on the nonlinear stability and obtained significant results.
