On a planar circular restricted charged three-body problem

Abstract

We introduce a circular restricted charged three-body problem on the plane. In this model, the gravitational and Coulomb forces, due to the primary bodies, act on a test particle; the net force exerted by some primary body on the test particle can be attractive, repulsive or null. The restricted problem is obtained by the general planar charged three-body problem considering one mass of the three bodies going to zero. We obtain necessary restrictions for the parameters that appear in the problem, in order to be well defined. Taking into account such restriction, we study the existence and linear stability of the triangular equilibrium solutions, as well as its location in the configuration space. We also obtain necessary and sufficient conditions for the existence of the collinear equilibrium solutions.

The Asymptotic Behavior of Solutions to the Repulsive $n$-Body Problem

“…The estimate for E pot (t) follows directly from part (b) of the theorem. It implies the lower bound in (2), while the upper bound is obvious from the bound for the velocities in (4).…”

“…The repulsive n-body problem, which can also be viewed as a special case of the so-called charged n-body problem with the repulsive Coulomb interaction dominating the Newtonian gravitational attraction, and which is certainly less important and less intriguing than the classical, gravitational n-body problem, appears in various places in the literature. In addition to [6] we mention [1,2,3,4,7,8].…”

Effect of variation of charge in the circular restricted three-body problem with variable masses

“…In view of the study of the stability of the equilibrium points, we determine numerically the roots of Equation (13). Table 1 gives the roots of Equation (13) for the different values of the equilibrium points.…”

“…They observed that the displacement around the triangular equilibrium points is not stable. More recently, Bengochea et al [13] investigated the location and the stability of the equilibrium points of the circular restricted charged three-body problem in a plane. Abouelmagd et al [14] studied the location of the out of plane, equilibrium points in the special case of a non-isotropic variation of the mass in the restricted three-body problem.…”

Dynamics in the Charged Restricted Circular Three-Body Problem

“…Points (0, 0, ±L) correspond to the circular orbits, the circle a 3 = 0 (the equator) accounts for the collision orbits, and the other points on the sphere refer to elliptic motions. Hamiltonian (5) in terms of the invariants reads as (8) H…”