Search

The research presented in this work focuses on investigating the characteristics of equilibrium points within the context of the photogravitational restricted three-body problem. Specifically, the study considers the influences of albedo effect, a straight segment, radiation pressure, as well as small perturbations in the Coriolis and centrifugal forces. The dynamical model proposed in this study reveals the presence of five equilibrium points. Among these, three are collinear with the centers of the massive bodies, while the remaining two are non-collinear. By examining various parameters involved in the system, the effect on the position of the equilibrium points is explored through numerical and graphical analysis. These investigations provide valuable insights into how the positions of these points are affected by changes in the parameters. Another significant aspect addressed in this research is the stability of the equilibrium points. The study finds that the collinear equilibrium points are unstable, irrespective of the parameters involved. On the other hand, the non-collinear points exhibit stability within a specific range of the mass parameter. The precise range of stability depends on the values of the other parameters present in the system. Additionally, the research delves into the study of the permissible and forbidden regions of motion for an infinitesimal body within the system. This analysis is conducted by considering different values of the Jacobian constant and it suggests that the Jacobian constant significantly influences the dynamics of the system and has a direct impact on the permissible regions of motion of the infinitesimal body. [ABSTRACT FROM AUTHOR]

The present investigation deals with the outcomes of the small perturbations σ 1 and σ 2 in the Coriolis and centrifugal forces respectively, in the oblate straight segment setup of the restricted 2 + 2 body problem. We describe the dynamical system that consists of the primaries of masses m 1 and m 2 as oblate spheroid and straight segment, respectively. With this setup, we obtain the equations of motion of the infinitesimal bodies having masses m 3 and m 4 under the gravitational attraction of the primary bodies, their mutual attraction and the small perturbations in the Coriolis and centrifugal forces. We determine the equilibrium points by using the perturbation technique in the equilibrium points for the case m 4 = 0 . We get fourteen equilibrium points, six of which are on the line connecting the centers of the primaries and eight of which lie on the x y - plane but not on the x - axis. The stability of the equilibrium points for a particular set of the parameters is analyzed and it is concluded that the collinear equilibrium points are unstable. The four non-collinear equilibrium points are stable for some combinations of σ 1 and σ 2 and rest are unstable for all values of σ 1 and σ 2 . The permissible and forbidden regions of motion of the infinitesimal body are also studied for the different values of the Jacobian constant and it is perceived that the permissible regions of motion expands on decreasing the value of the Jacobian constant. These regions are subsequently affected by the involvement of the mass, oblateness, length and perturbations in the Coriolis and centrifugal forces parameters. [ABSTRACT FROM AUTHOR]

The fractal basins of convergence (BoC) linked with the equilibrium points are explored in the (N + 1)− body ring problem under the effect of small perturbations in the Coriolis and centrifugal forces when the bodies are sources of radiation. The evolution of the positions and the stability of the libration points and the possible regions of motion are determined as the function of mass parameter, the Coriolis, and centrifugal and radiation parameters. In addition, the parametric variation of the effect of the small perturbations in the Coriolis and centrifugal forces on the stability of the equilibrium points are also illustrated numerically. The multivariate version of the Newton–Raphson(NR) iterative method is used to analyze the effect of the radiation parameters and mass parameter on the topology of the BoC. [ABSTRACT FROM AUTHOR]

We have studied the restricted four-body problem (R4BP) with the effect of the small perturbation in the Coriolis and centrifugal forces on the libration points and zero velocity curves (ZVCs). Further, we have supposed that all the primaries are set in an equilateral triangle configuration, moving in the circular orbits around their common centre of mass. We have observed that the effect of the small perturbation in centrifugal force has a substantial effect on the location of libration points but a small perturbation in the Coriolis force has no impact on the location of libration points. But the stability of the libration points is highly influenced by the effect of the small perturbation in the Coriolis force. It is observed that as the Coriolis parameter increases, the libration points become stable. Further, it is found that the effect of the small perturbation in the centrifugal force has a substantial influence on the regions of possible motion. Also, when the effect of small perturbation in the centrifugal force increases the forbidden region decreases; here the motion is not possible for the infinitesimal mass. It is observed when the value of the Jacobian constant decreases, the regions of possible motion increase. In addition, we have also discussed how small perturbations in the Coriolis and centrifugal forces influence the Newton-Raphson basins of convergence. [ABSTRACT FROM AUTHOR]

In this problem, one of the primaries of mass m1 is a Roche ellipsoid filled with a homogeneous incompressible fluid of density ρ1. The smaller primary of mass m2 is an oblate body outside the Ellipsoid. The third and the fourth bodies (of mass m3 and m4 respectively) are small solid spheres of density ρ3 and ρ4 respectively inside the Ellipsoid, with the assumption that the mass and the radius of the third and the fourth body are infinitesimal. We assume that m2 is describing a circle around m1. The masses m3 and m4 mutually attract each other, do not influence the motions of m1 and m2 but are influenced by them. We have extended the Robe’s restricted three-body problem to 2+2 body problem under the assumption that the fluid body assumes the shape of the Roche ellipsoid (Chandrashekhar in Ellipsoidal figures of equilibrium, Chap. 8, Dover, New York, 1987 ). We have taken into consideration all the three components of the pressure field in deriving the expression for the buoyancy force viz (i) due to the own gravitational field of the fluid (ii) that originating in the attraction of m2 (iii) that arising from the centrifugal force. In this paper, equilibrium solutions of m3 and m4 and their linear stability are analyzed. We have proved that there exist only six equilibrium solutions of the system, provided they lie within the Roche ellipsoid. In a system where the primaries are considered as Earth-Moon and m3, m4 as submarines, the equilibrium solutions of m3 and m4 respectively when the displacement is given in the direction of x1-axis or x2-axis are unstable. [ABSTRACT FROM AUTHOR]

• The modified circular restricted three-body problem has been studied. • The parametric evolution of the stationary points are illustrated. • The effect of the Coriolis and centrifugal force on the stationary points and their stability are unveiled. • The multivariate version of the NR-iterative scheme is used to discuss the basins of convergence. In the present manuscript, the effects of small perturbations in the centrifugal and Coriolis forces with additional effect of three-body interaction on the locations as well as stability of the stationary points (SPs), and on the topology of the basins of convergence (BoCs) linked with these SPs in the restricted three-body problem (R3BP) are discussed by using the multivariate version of the Newton-Raphson iterative scheme. It is found that the positions of the SPs are highly influenced by the centrifugal force but their stability is highly influenced by combinations of the centrifugal and Coriolis forces. In addition, the correlations betwixt the basin of convergence (BoC) connected to the SPs and the associated number of iterations needed to assure pre-assumed precision are analyzed. Our analysis suggests that the mass ratio μ , three-body interaction parameter k and the effect in centrifugal and the Coriolis forces controlled by parameters ϕ and φ are very influential parameters. [ABSTRACT FROM AUTHOR]

The present study is motivated by the work of Abouelmagd et al. (Int J Geom Methods Mod Phys 18(4):21500055, 2020), that it is generalized by considering the effect of small perturbations in the Coriolis and centrifugal forces on the location and stability of the equilibrium points in the Robe's restricted three-body problem. The problem possesses a pair of collinear equilibrium points and an infinite number of non-collinear equilibrium points. All of the resulting equilibrium points are subjected to a linear stability study. It has been observed that the locations and stability are guaranteed to be influenced by the perturbations in the Coriolis and centrifugal forces. Furthermore, a numerical study has been carried out to observe how the perturbing parameters affect the position and stability of the equilibrium points. [ABSTRACT FROM AUTHOR]

In the framework of photogravitational version of the restricted five-body problem, the existence and stability of the in-plane equilibrium points, the possible regions for motion are explored and analysed numerically, under the combined effect of small perturbations in the Coriolis and centrifugal forces. Moreover, the multivariate version of the Newton-Raphson iterative scheme is applied in an attempt to unveil the topology of the basins of convergence linked with the libration points as function of radiation parameters, and the parameters corresponding to Coriolis and centrifugal forces. [ABSTRACT FROM AUTHOR]

In the present problem, we have studied the effect of small perturbations in the Coriolis and centrifugal forces on the locations and stability of libration points by taking the smaller primary as radiating oblate spheroid in the restricted four‐body problem. We have supposed that all the primaries are set in an equilateral triangle configuration, moving in circular orbit around their common center of mass. We have observed that the oblateness and radiation of the third primary, and the effect of the small perturbation in centrifugal force have substantial influences on the locations of libration points but the effect of the small perturbation in the Coriolis force has no impact on their locations. However, the stability of the libration points is highly influenced by the effect of the small perturbation in the Coriolis force. Furthermore, it is obtained that the effect of the small perturbation in the centrifugal force has a substantial influence on the regions of possible motion. In addition, we have also discussed how the oblateness and radiation pressure of the third primary, and the small perturbations in the Coriolis and centrifugal forces influence geometry of the basins of convergence by using multivariate version of the Newton–Raphson iterative scheme. [ABSTRACT FROM AUTHOR]

In the framework of the axisymmetric problem of restricted five bodies, the existence and stability of the libration points, the regions of possible motion are illustrated and analyzed numerically, under the effect of small perturbations in the Coriolis and centrifugal forces. It is explored how the parameters influence substantially the positions of the libration points and the possible regions of motion. In an attempt to understand how the parameters involved due to the small perturbations in the Coriolis and centrifugal forces affect the stability of the libration points, we perform a systematic investigation and reveal that some of the collinear and non-collinear libration points are stable under these perturbations, whereas none of these libration points are stable for any combination of the angle parameters when the effects of these forces are neglected. [ABSTRACT FROM AUTHOR]