Existence of equilibrium points in the magnetic binary problem with variable mass

Mohd Arif

doi:10.28919/jmcs/3482

Abstract

The present paper deals with the existence of equilibrium points in the magnetic binary problem when the infinitesimal body is of variable mass. We have observed that there exists nine collinear and two non-collinear equilibrium points we have also observed that the mass reduction factor has a significant role on the existence of the equilibrium points.https://doi.org/10.28919/jmcs/3482

Highlights

In 1928 Jeans [7] has studied the two-body problem with variable mass
The present paper deals with the existence of equilibrium points in the magnetic binary problem when the infinitesimal body is of variable mass
We have observed that the these points have the different positions for different values of mass reduction factor γ and small values of μ and for L1 and L2 this variation tends to zero as μ increases and γ decreases but for L3 this variation increases as μ increases and γ decreases The combine position of L1 L2 and L3 shows in fig (4)

Summary

Introduction

In 1928 Jeans [7] has studied the two-body problem with variable mass. Omarov [13] has discussed the restricted problem of perturbed motion of two bodies with variable mass. Singh et al [6] has discussed the non-linear stability of equilibrium points in the restricted three body with variable mass. Jagdish Singh [5] discussed the photogravitational restricted three body problem with variable mass. Hassan et al [4] has studied the existence of equilibrium points in the restricted three body problem with variable mass when the smaller primary is an oblate spheroid. In this article we have discussed the motion of a charged particle of variable mass which is moving in the field of two rotating magnetic dipoles

Equation of motion

Primaries participate in the circular motion around their centre of mass

Existence of Equilibrium Points

Conclusion