Efficient computational approaches to obtain periodic orbits in Hamiltonian systems: application to the motion of a lunar orbiter

Dena, Ángeles; Abad, Alberto; Barrio, Roberto

doi:10.1007/s10569-015-9651-2

Cited by 6 publications

(1 citation statement)

References 36 publications

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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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