scholarly journals A Special Case of Central Configuration for Planar Concave 5-body Problem with Newtonian Potentials

2020 ◽  
Vol 07 (04) ◽  
pp. 40-45
Author(s):  
Yangshanshan LIU
1979 ◽  
Vol 81 ◽  
pp. 23-28
Author(s):  
John D. Hadjidemetriou

It is known that families of periodic orbits in the general N-body problem (N≥3) exist, in a rotating frame of reference (Hadjidemetriou 1975, 1977). A special case of the above families of periodic orbits are the periodic orbits of the planetary type. In this latter case only one body, which we shall call sun, is the more massive one and the rest N-1 bodies, which we shall call planets, have small but not negligible masses. The aim of this paper is to study the properties of the families of periodic planetary-type orbits, with particular attention to stability. To make the presentation clearer, we shall start first with the case N=3 and we shall extend the results to N>3. We shall discuss planar orbits only.


2014 ◽  
Vol 9 (S310) ◽  
pp. 106-107 ◽  
Author(s):  
Winston L. Sweatman

AbstractThe general four-body problem can be simplified by considering the special case where the system contains two pairs of identical masses and is symmetrical. The simple models that occur may aid our understanding of the general problem. Systems that arise from Schubart-like interplay orbits are an important feature of the dynamics.


1975 ◽  
Vol 1 (1) ◽  
pp. 29-40 ◽  
Author(s):  
T. M. Lennon

Occasionalism is often taken by historians of philosophy to have been an ad hoc hypothesis to establish the mind-body causal connections which on Cartesian principles are thought otherwise impossible. My aim in this paper is to show that this view is utterly without historical foundation, that, on the contrary, the view that only God can be a real cause of mind-body interaction was but a special case of a claim argued on grounds transcending the mind-body problem, and, what will be part of this, that the logical character of occasionalism anyhow precluded it from the role into which it was later miscast. More specifically, I shall show that occasionalism was but a consequence of the metaphysics adopted by the Cartesians in their general account of change. Though the same case could be made for the views of Clauberg and Geulincx, my concern will be with the occasionalism of Malebranche. My case here will be that his view is the historical and logical dénouement of principles more or less explicit both in Descartes and in two of his lesser known disciples, LaForge and Cordemoy.


BIBECHANA ◽  
2014 ◽  
Vol 11 ◽  
pp. 149-156
Author(s):  
RR Thapa

The Sitnikov's problem is a special case of restricted three body problem if the primaries are of equal masses (m1 = m2 = 1/2) moving in circular orbits under Newtonian force of attraction and the third body of mass m3 moves along the line perpendicular to plane of motion of primaries. Here oblate spheroid primaries are taken. The solution of the Sitnikov's circular restricted three body problem has been checked when the primaries are oblate spheroid. We observed that solution is depended on oblate parameter A of the primaries and independent variable τ = ηt. For this the stability of non-trivial solutions with the characteristic equation is studied. The general equation of motion of the infinitesimal mass under mutual gravitational field of two oblate primaries are seen at equilibrium points. Then the stability of infinitesimal third body m3 has been calculated. DOI: http://dx.doi.org/10.3126/bibechana.v11i0.10395 BIBECHANA 11(1) (2014) 149-156


2003 ◽  
pp. 43-46 ◽  
Author(s):  
V. Mioc ◽  
M. Barbosu

We tackle the two-body problem associated to H?non-Heiles? potential in the special case of the collision singularity. Using McGehee-type transformations of the second kind, we blow up the singularity and replace it by the collision manifold Mc pasted on the phase spece. We fully describe the flow on Mc. This flow is similar to analogous flows met in post-Newtonian two-body problems.


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