On the photogravitational R4BP when the third primary is a triaxial rigid body

On the Newton–Raphson basins of convergence associated with the libration points in the axisymmetric restricted five-body problem: The concave configuration

“…An interesting phenomenon is also observed that the extent of basins of convergence corresponding to the collinear libration point L 11 is infinite whereas, for all the other libration point, the domains of basins of convergence are finite. Further, it is also observed that most of the area in the configuration plane (x, y) is covered by the finite domain of the basins of convergence corresponding to the libration points L 8,9,10 in which L 8,9 are symmetrical with respect to x−axis and L 10 encloses the topology of the basins of convergence associated with finite domains. The basins of convergence linked with the libration points L 1,6,7 alike butterfly with wings and many antennas in which L 6,7 are symmetrical with respect to x−axis and cover more area than the area covered by L 1 .…”

“…Thus, the Newton-Raphson iterative scheme to determine the basins of convergence associated with the libration points, provides intrinsic properties of the dynamical system. A series of literature is available which deals with the basins of convergence associated with the libration points in various type of dynamical system such as the restricted three-body problem (e.g., [29], [24]), the restricted four-body problem with and without various perturbations (e.g., [15], [8], [9], [20,21], [30,31], [22]), the restricted five-body problem (e.g., [34]), the Hill's problem (e.g., [10], [33]), pseudo-Newtonian three and four body problem (e.g., [32], [25]), the Copenhagen problem (e.g., [35], [23]), or even the Sitnikov Problem in three and four body problem (e.g., [11], [36,37]). The present paper is described with following structure: the basic properties of the model of axisymmetric five-body problem are presented in Sect.2.…”

Divulging the effect of small perturbations in the Coriolis and centrifugal forces in the photogravitational version of autonomous restricted four‐body problem with oblate primary

“…The study of the existence of periodic orbits in the restricted four‐body problem fascinated many researchers in recent time: some of them are Alvarez‐Ramírez & Barrabés (), Baltagiannis & Papadakis (), Papadakis (), Burgaos‐Garcia & Delgado ()). Furthermore, the existence and stability of equilibrium points in the restricted four‐body problem are studied and presented in a series of research articles: Kumari & Kushvah (), Asique et al (), Asique et al (), Papadouris & Papadakis (), and Singh & Vincent (). The effect of small perturbations in the Coriolis and centrifugal forces on the stability of libration points in the restricted four‐body problem is studied by Singh & Vincent ().…”

The effect of small perturbations in the Coriolis and centrifugal forces on the existence of libration points in the restricted four‐body problem with variable mass

“…It is well known that R4BP has at most 10 libration points, out of which 2 or 4 are collinear with the dominant primary and rest are non-collinear. Many mathematicians and astronomers have studied the classical R4BP including various perturbations in recent years: the determination of the locations and stability of the libration points in the R4BP (see e.g., Asique et al 2016;Asique et al 2017;Papadakis 2015;Kalvouridis et al 2007;Kalvouridis & Hadjifotinou 2008;Papadakis 2007;Papadakis 2016). A new kind of problem, referred as the Robe's restricted problem of 2 + 2 bodies, was studied by Kaur & Aggarwal (2012 and .…”