On some new aspects of the photo-gravitational Copenhagen problem

Kalvouridis, T. J.

doi:10.1007/s10509-008-9861-0

Cited by 20 publications

(21 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This subsection is devoted to the case when e ∈ (−0.19526, −0.173395), where eleven libration points exist: five on the x−axis (L 1,2,4,6,7 ) in which L 4 is the central libration point, two on y−axis (L 8,9 ) and four on (x, y) plane (L 10,11,12,13 ). The evolution of the basins of convergence, using Newton-Raphson iterative scheme, for three values of parameter e are illustrated in Fig.…”

Section: Case Iii: When Eleven Libration Points Existmentioning

confidence: 99%

“…Moreover, the butterfly wing shaped domains of convergence associated with the libration points L 8,9 shown in purple and crimson color exist. The most notable change due to existence of eight extra libration points in the presence of a negative value of the parameter is the following four lobe appear, corresponding to non collinear libration points (L 10,11,12,13 ) in the vicinity of the primaries as well as at the back of both the exotic bugs. Let us denote the region at the back of exotic bugs corresponding to the libration points L 1 (yellow) and L 7 (cyan) by R 1 and R 7 respectively.…”

Section: Case Iv: When Thirteen Libration Points Existmentioning

confidence: 99%

“…Therefore, the basic configuration of the Copenhagen problem can have a real application in which the third body may be considered as a "Trojan" asteroid, moving in the vicinity of two main bodies. There are two versions of the Copenhagen problem: (i) the original version of the Newtonian gravitational attraction (e.g., [1]; [14]; [2]; [12,13]; [16]; [22]) and (ii) the modified version in which the effective potential have been modified by introducing other perturbing parameters. More precisely, the pseudo-Newtonian planar restricted three-body problem deals with the modified version, where additional general relativistic corrections have been included to the effective potential ( [24]).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fractal basins of convergence of libration points in the planar Copenhagen problem with a repulsive quasi-homogeneous Manev-type potential

Suraj

Zotos

Kaur

et al. 2018

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

The Newton-Raphson basins of convergence, corresponding to the coplanar libration points (which act as attractors), are unveiled in the Copenhagen problem, where instead of the Newtonian potential and forces, a quasi-homogeneous potential created by two primaries is considered. The multivariate version of the Newton-Raphson iterative scheme is used to reveal the attracting domain associated with the libration points on various type of two-dimensional configuration planes. The correlations between the basins of convergence and the corresponding required number of iterations are also presented and discussed in detail. The present numerical analysis reveals that the evolution of the attracting domains in this dynamical system is very complicated, however, it is a worth studying issue.

show abstract

Section: Case Iii: When Eleven Libration Points Existmentioning

confidence: 99%

Section: Case Iv: When Thirteen Libration Points Existmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fractal basins of convergence of libration points in the planar Copenhagen problem with a repulsive quasi-homogeneous Manev-type potential

Suraj

Zotos

Kaur

et al. 2018

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

show abstract

“…This means that the corresponding radiation coefficient b has a unique value that characterizes a particular particle. Figure 8 shows the distribution of the equilibria in two cases of the Copenhagen problem (see also [46]) …”

Section: The Photo-gravitational Versionmentioning

confidence: 99%

The ring problem of (N+1) bodies: ten years of research (1999–2009)

Kalvouridis

2009

SPIE Proceedings

View full text Add to dashboard Cite

One of the most popular N-body models that has been under investigation in the last ten years, is the so-called ring problem of (N+1) bodies, otherwise known as the regular polygon problem of (N+1) bodies. Here we present an overview of the scientific work that has been done throughout these years as well as the major results obtained so far. An extended bibliography is displayed at the end of this article, aiming to become a source of information for further analytical study. 1． INTRODUCTIONThe ring problem of (N+1) bodies describes the motion of a small body S which moves in the force field created by N major bodies called the primaries. The ν=N-1 of them, have equal masses and are located at the vertices of an imaginary ν-gon. The N-th body has a different mass and is located at the center of mass of this formation (Figure 1). Figure 1. The general configuration of the ring problem of (N+1) bodiesThe problem is characterized by two parameters: the number ν of the peripheral primaries and the mass parameter β which is the ratio of the central mass m 0 to a peripheral one named m. The regular polygon formation of the big bodies with another one at their center of mass was proposed by Maxwell in 1865 [1] in order to explain the rings of Saturn. Since then, this configuration has often been found to be the center of special scientific interest and many papers have been written aiming to prove its central character and to find homographic solutions, relative equilibria, conditions for stability etc. not only for the simple gravitational case but also for cases that include post-Newtonian potentials ([2]-[21]). However, the ring problem as a new dynamical system under the description made at the beginning of this paragraph, first appeared in Scheeres' PhD Thesis ([22]) and a little later in a joint paper with Vinh ([23]). The problem was considered anew by the author of the present articles and his collaborators, who devoted ten years (1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009) of scientific research in investigating many of its aspects ([24] -[48]). He reformulated the whole problem and he improved the original model by considering not only gravitational forces but also forces coming either from radiation or from post-Newtonian potentials. He also examined some cases where the small body is a tri-axial body or a gyrostat. The configuration is quite simple and, apart from other benefits, can be reduced to some already known problems-models of

show abstract

“…The literature is replete of papers on the basins of attraction in several types of dynamical systems. In the vast majority of them the Newton-Raphson iterative scheme (which is the simplest one) is used for revealing the convergence properties in several dynamical systems such as the Sitnikov problem (e.g., Douskos et al, 2012), the Hill problem with oblateness and radiation pressure (e.g., Douskos, 2010;Zotos, 2017b), the circular restricted three-body problem with oblateness and radiation pressure (e.g., Zotos, 2016), the Copenhagen problem with radiation pressure (e.g., Kalvouridis, 2008), the pseudo-Newtonian planar circular restricted threebody problem (e.g., Zotos, 2017c), the circular restricted four-body problem (e.g., Baltagiannis & Papadakis, 2011;Kumari & Kushvah, 2014;Zotos, 2017a,d), the circular restricted four-body problem with radiation pressure (e.g., Asique et al, 2016), the circular restricted four-body problem with various perturbations (e.g., Suraj et al, 2017a,b), the circular restricted five-body problem (e.g., Zotos & Suraj, 2018), the ring problem of N + 1 bodies (e.g., Croustalloudi & Kalvouridis, 2007;Gousidou-Koutita & Kalvouridis, 2009), or even the restricted 2+2 body problem (e.g., Croustalloudi & Kalvouridis, 2013).…”

mentioning

confidence: 99%

Comparing the basins of attraction for several methods in the circular Sitnikov problem with spheroid primaries

Zotos

2018

Astrophys Space Sci

View full text Add to dashboard Cite

The circular Sitnikov problem, where the two primary bodies are prolate or oblate spheroids, is numerically investigated. In particular, the basins of convergence on the complex plane are revealed by using a large collection of numerical methods of several order. We consider four cases, regarding the value of the oblateness coefficient which determines the nature of the roots (attractors) of the system. For all cases we use the iterative schemes for performing a thorough and systematic classification of the nodes on the complex plane. The distribution of the iterations as well as the probability and their correlations with the corresponding basins of convergence are also discussed. Our numerical computations indicate that most of the iterative schemes provide relatively similar convergence structures on the complex plane. However, there are some numerical methods for which the corresponding basins of attraction are extremely complicated with highly fractal basin boundaries. Moreover, it is proved that the efficiency strongly varies between the numerical methods.

show abstract

On some new aspects of the photo-gravitational Copenhagen problem

Cited by 20 publications

References 38 publications

Fractal basins of convergence of libration points in the planar Copenhagen problem with a repulsive quasi-homogeneous Manev-type potential

Fractal basins of convergence of libration points in the planar Copenhagen problem with a repulsive quasi-homogeneous Manev-type potential

The ring problem of (N+1) bodies: ten years of research (1999–2009)

Comparing the basins of attraction for several methods in the circular Sitnikov problem with spheroid primaries

Contact Info

Product

Resources

About