Advances in Astrophysics

Download PDF (910.3 KB) PP. 52 - 65 Pub. Date: February 1, 2017

DOI: 10.22606/adap.2017.21006

• Ram Kishor^*
  Central University of Rajasthan, NH-8, Bandarsindari, Kishangarh-305817, Dist.-Ajmer (Rajasthan), India
• Badam Singh Kushvah
  Department of Applied Mathematics, Indian School of Mines, Dhanbad 826004, Jharkhand, India

The stability properties, dynamical processes and factors affecting these are very important aspects to describing the behaviour of a dynamical system because these play a significant role in the study of their past evolution. The present article discuss about the existence of collinear equilibrium points, their computation and stability analysis in the Chermnykh-Like problem under the influence of perturbations in the form of radiation pressure, oblateness and a disc. In the presence of the disc, there exists a new collinear equilibrium point in addition to the three points of the classical problem. We examine the linear stability of the collinear equilibrium points with respect to disc’s outer radius b instead of mass parameter μ and it is found that all the collinear equilibrium points are unstable except L₃ which is stable for b ∈ (1.3312, 1.5275) provided that remaining parameters are fixed. Further, we obtain stability regions and perturbed mass ratio in the case of three main resonances for L₃ under appropriate approximations. We analyze the effect of the perturbations numerically and it is observed that they significantly affect the motion of infinitesimal mass. The results are limited up to the regular symmetric disc and the radiation effect of the bigger primary but further it can be extended for more generalized cases.

Chermnykh-Like problem, collinear equilibrium points, disc, linear stability, resonances.

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