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

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