Trajectories and Stability Regions of the Lagrangian Point $L_1$ in the Generalized Chermnykh-Like Problem

The Lagrange point $L_1$ for the Sun-Earth system is considered due to its special importance for the scientific community for the design of space missions. The location of the Lagrangian points with the trajectories and stability regions of $L_1$ are computed numerically for the initial conditions very close to the point. The influence of belt, effect of radiation pressure due to Sun and oblateness effect of second primary(finite body Earth) is presented for various values of parameters. The collinear point $L_1$ is asymptotically stable within a specific interval of time $t$ correspond to the values of parameters and initial conditions.