Stability Of L4 Research Articles

English

English

English

English

The locations of triangular equilibrium points in elliptic restricted three-body problem under the oblateness and radiation Effects

The Restricted Three-Body Problem (R3BP) considers motion of a third infinitesimal object under the gravitational influences of the primaries (bigger and smaller massive bodies) whose orbits are around the center of mass. If the orbits are elliptical, this belongs to Elliptic R3BP (ER3BP). In planar case it possesses five equilibrium points consisting of three collinear (L1, L2, and L3) and two triangular (L4 and L5). To mimic a better astrophysical R3BP, such as motion of a satellite in star-planet system, the classical problem can be generalized by considering the effects of radiation pressure and oblate spheroid shape on the primaries. We study analytically the locations and the stability of L4 and L5 equilibrium points in the frame of ER3BP with incorporating the effects of radiation for bigger primary and oblateness for smaller primary. Our study suggests that the oblateness factor (A2) and the radiation factor (q1) shift the positions of L4 and L5 points compared with the classical ones. We also find that there is a stability limit for motion of the third body around these points.

The Nonlinear Stability of L 4 in the R3BP when the Smaller Primary is a Heterogeneous Spheroid

We have investigated the nonlinear stability of the triangular libration point L 4 in the R3BP when the smaller primary is a heterogeneous spheroid with three layers having different densities. We observe that in the nonlinear sense, the triangular libration is stable in the range of linear stability 0<μ<μ c , a critical value of mass parameter μ, except for three mass ratios $\mu _{1}^{\prime },\mu _{2}^{\prime }$ , $\mu _{3}^{\prime }$ at which Moser’s theorem is not applicable.

On the stability of L4,5 in the perturbed relativistic R3BP with a triaxial bigger primary

In the present paper, we endeavor to study the stability of triangular points under the influence of small perturbations in the Coriolis and centrifugal forces, together with the triaxiality of the bigger primary in the framework of the relativistic R3BP. It is observed that the locations of these points are affected by the relativistic factor, triaxiality and a small perturbation in the centrifugal force, but are unaffected by that of the Coriolis force. It is also seen that for these points the range of stability region increases or decreases according as equation (14) without is greater or less than zero.

New insights into the stability of L4 in the spatial restricted three-body problem

New insights into the stability of L4 in the spatial restricted three-body problem

Effect of oblateness on the non-linear stability of L 4 in the restricted three-body problem

Non-linear stability of the libration point L 4 of the restricted three-body problem is studied when the more massive primary is an oblate spheroid with its equatorial plane coincident with the plane of motion, Moser's conditions are utilised in this study by employing the iterative scheme of Henrard for transforming the Hamiltonian to the Birkhoff's normal form with the help of double D'Alembert's series. It is found that L 4 is stable for all mass ratios in the range of linear stability except for the three mass ratios: $$\begin{gathered} \mu _{c1} = 0.0242{\text{ }}...{\text{ }}{}^{{\text{\_\_}}}0.1790{\text{ }}...{\text{ }}A_1 , \hfill \\ \mu _{c2} = 0.0135{\text{ }}...{\text{ }}{}^{{\text{\_\_}}}0.0993{\text{ }}...{\text{ }}A_1 , \hfill \\ \mu _{c3} = 0.0109{\text{ }}...{\text{ }}{}^{{\text{\_\_}}}0.0294{\text{ }}...{\text{ }}A_1 . \hfill \\ \end{gathered} $$

Computer algebra, Lie Transforms and the nonlinear stability of L4

Computer algebra, Lie Transforms and the nonlinear stability of L4

Stability of L4 and L5 against radiation pressure

Stability of L4 and L5 against radiation pressure

Stability of and motion aboutL 4 at three-to-one commensurability

The stability ofL 4 and the motion aboutL 4 in the restricted problem of three bodies is investigated when there is three-to-one commensurability between the long and short periods of motion, that is, when the mass ratio μ has the value μ=μ0.013516.... The two time scale method is used (1) to show thatL 4 is an unstable equilibrium point when μ=μ3, (2) to determine for what initial conditions periodic orbits occur when μ≈μ3, (3) to determine the stability of the periodic orbits, and (4) to investigate the boundedness of the motions aboutL 4 when μ≈μ3.