Stability analysis in the perturbed CRR3BP finite straight segment model under the effect of viscosity

Abstract

In this paper Robe-finite straight segment model is analyzed under the effects of viscosity and perturbations in the Coriolis and centrifugal forces. We have taken the first primary $P_{1}$ as a rigid spherical shell $m_{1}$ filled with viscous, homogeneous incompressible fluid of density $\rho _{1}$, and the second primary $P_{2}$ as a finite straight segment of length $2l$. A third body of mass $m_{3}$, moving inside $m_{1}$ is a small solid sphere of density $\rho _{3}$. We prove how the locations of equilibrium points $L_{i}, i=1,2,\ldots ,5$ are affected by the presence of perturbation in the centrifugal force. However, these remain unaffected by the viscosity and perturbation in the Coriolis force. The stability criteria for $L_{1,2}$ are investigated and it has been observed that their stability is affected by the viscosity and perturbation of the centrifugal force. It is prominently observed that the viscosity changes their nature of stability from being stable to asymptotically stable. The equilibrium points $L_{3,4,5}$ are unstable irrespective of the perturbation and viscosity.