Bifurcations From Planar to Three-Dimensional Periodic Orbits in the Photo-Gravitational Restricted Four-Body Problem

Kalvouridis, T. J.; Hadjifotinou, K. G.

doi:10.1142/s0218127408020392

Cited by 17 publications

(4 citation statements)

References 9 publications

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“…For our investigation we adopt Radzievskii's simplifying theory (1950Radzievskii's simplifying theory ( , 1951 that has been used by many investigators (Bhatnagar and Chawla 1979;Manju and Choudhry 1985;Simmons et al 1985;Luk'yanov 1987Luk'yanov , 1988Choudhry 1988, 1989;Perezhogin and Tureshbaev 1989;El-Shaboury 1990;Ragos and Zagouras 1991;Niedzielska 1994;Ragos and Zafiropoulos 1995;Kunitsyn and Polyakhova 1995;Elipe and Lara 1997;Kalvouridis 1999;Markellos et al 2000;Ishwar and Elipe 2001;Perdios et al 2001;Perdios 2003;Kazazakis and Kalvouridis 2004;Papadakis 2006aPapadakis , 2006bKalvouridis et al 2007;Kalvouridis and Hadjifotinou 2008;etc. ) and is based on some assumptions that can be summarized as follows:…”

Section: Equations Of Motionmentioning

confidence: 99%

On some new aspects of the photo-gravitational Copenhagen problem

Kalvouridis

2008

Astrophys Space Sci

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We deal with some new aspects of the photogravitational Copenhagen case of the restricted three-body problem; more particularly, the distribution and the attracting domains of the stationary solutions of small particles that move in the neighborhood of two major bodies with equal masses when one or both primaries are radiation sources with constant luminosity. Under these conditions, each particle is subjected not only to gravitational forces but to the radiation emitted from the primaries as well.

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Section: Equations Of Motionmentioning

confidence: 99%

On some new aspects of the photo-gravitational Copenhagen problem

Kalvouridis

2008

Astrophys Space Sci

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“…The great importance of the periodic solutions in a dynamical system is revealed through the immense work on this field of celestial mechanics (see e.g., Arenstrorf 1963; Barrar 1965; Boccaletti & Pucacco 1996a, 1996b; Brjuno 1978, 1994; Broucke 1968; Danby 1962; Darwin 1911; Deprit & Henrard 1965; Hadjidemetriou 1975; Hagihara 1970; Hénon 1965a, 1965b, 1973, 1974, 1997, 2001; Markellos et al 1974; Marshal 1990; Moulton 1920, 1970; Perko 1981; Strömgren 1935; Szebehely 1967; Wintner 1947). More recent articles on locating families of periodic orbits are the works of Barrio & Blesa (2009); Barrio et al (2009); Barrio & Rodriguez (2014); Croustalloudi & Kalvouridis (2008); Dena et al (2016); Hadjifotinou & Kalvouridis (2005); Kalvouridis et al (2007); and Kalvouridis & Hadjifotinou (2008, 2011).…”

Section: Introductionmentioning

confidence: 99%

Networks of planar symmetric periodic orbits in a barred galaxy model

et al. 2020

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We present the networks of planar symmetric periodic orbits in a single barred galaxy model. More specifically, we determine how the numerical value of the bar's semimajor axis affects not only the positions but also the linear stability of the periodic solutions. The atlas of the periodic orbits, with multiplicity up to 10, is presented on the (x, E) plane so as to be able to understand the importance of the total orbital energy on the periodic networks. For every orbital family, we also compute the horizontal and vertical critical solutions of the system, from which new periodic families bifurcate. Our analysis indicates that several periodic families contain orbits, which qualify as x1 type orbits and stabilize the barred structure of the galaxy. Furthermore, the numerical results suggest that the semimajor axis of the bar highly influences the overall orbital properties of the dynamical system.

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“…The nonlinear stability analysis in the R4BP was studied by Alvarez‐Ramirez et al (). The location of the periodic orbits in the R4BP is a very interesting topic (see e.g., Alvarez‐Ramirez & Barrabes ; Baltagiannis & Papadakis ; Kalvouridis et al ; Kalvouridis & Hadjifotinou ; Papadakis ; Papadakis ). A new kind of problem, referred as the Robe's restricted problem of 2 + 2 bodies, was studied by Kaur & Aggarwal (, , ) and Aggarwal & Kaur ().…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2018

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This paper shows the effect of small perturbations in the Coriolis and centrifugal forces in the restricted four‐body problem (R4BP) with variable mass. The existence, location, and stability of the libration points are investigated numerically and graphically under these perturbations. In the present problem, a fourth body with infinitesimal mass is moving under the Newtonian gravitational attraction of three primaries which are moving in a circular orbit around their common center of mass fixed at the origin of the coordinate system. Moreover, according to the solution of Lagrange, the primaries are fixed at the vertices of an equilateral triangle. The fourth body does not affect the motion of three primaries. Furthermore, the fourth body's mass varies according to Jeans' law. The equations of motion of the test particle, i.e., fourth body moving under the gravitational influence of the primaries, are derived. Throughout the paper, we consider the case where the primary body placed along the x‐axis is dominant while the other two small primaries are equal. Further, it is shown that there exist either 8 or 10 libration points out of which 2 or 4 are collinear with the dominating primary and the rest are non‐collinear for fixed values of the parameters. The linear stability of all the libration points under consideration is investigated, and these libration points are found to be unstable. The allowed regions of motion are determined by using the zero‐velocity surface, and the positions of the libration points on the orbital plane are presented. Moreover, by using the Newton–Raphson iterative scheme, we unveiled the effects of the Coriolis and centrifugal forces on the topology of the basins of convergence associated with the libration points.

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Bifurcations From Planar to Three-Dimensional Periodic Orbits in the Photo-Gravitational Restricted Four-Body Problem

Cited by 17 publications

References 9 publications

On some new aspects of the photo-gravitational Copenhagen problem

On some new aspects of the photo-gravitational Copenhagen problem

Networks of planar symmetric periodic orbits in a barred galaxy model

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

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