共查询到20条相似文献，搜索用时 31 毫秒
1.
Josep M. Cors Jaume Llibre Merce Ollé 《Celestial Mechanics and Dynamical Astronomy》2004,89(4):319-342
We study the planar central configurations of the 1 +n body problem where one mass is large and the other n masses are infinitesimal and equal. We find analytically all these central configurations when 2≤n≤4. Numerically, first we provide evidence that when n9 the only central configuration is the regular n-gon with the large mass in its barycenter, and second we provide also evidence of the existence of an axis of symmetry for
every central configuration.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
2.
Allyson Oliveira 《Celestial Mechanics and Dynamical Astronomy》2013,116(1):11-20
In this work we are interested in the central configurations of the planar $1+4$ body problem where the satellites have different infinitesimal masses and two of them are diametrically opposite in a circle. We can think of this problem as a stacked central configuration too. We show that the configurations are necessarily symmetric and the other satellites have the same mass. Moreover we prove that the number of central configurations in this case is in general one, two or three and, in the special case where the satellites diametrically opposite have the same mass, we prove that the number of central configurations is one or two and give the exact value of the ratio of the masses that provides this bifurcation. 相似文献
3.
New stacked central configurations for the planar 5-body problem 总被引：1，自引：0，他引：1
Jaume Llibre Luis Fernando Mello Ernesto Perez-Chavela 《Celestial Mechanics and Dynamical Astronomy》2011,110(1):43-52
A stacked central configuration in the n-body problem is one that has a proper subset of the n-bodies forming a central configuration. In this paper we study the case where three bodies with masses m
1, m
2, m
3 (bodies 1, 2, 3) form an equilateral central configuration, and the other two with masses m
4, m
5 are symmetric with respect to the mediatrix of the segment joining 1 and 2, and they are above the triangle generated by
{1, 2, 3}. We show the existence and non-existence of this kind of stacked central configurations for the planar 5-body problem. 相似文献
4.
In this paper we prove, for all p ≥ 2, the existence of central configurations of the pn-body problem where the masses are located at the vertices of p nested regular polyhedra having the same number of vertices n and a common center. In such configurations all the masses on the same polyhedron are equal, but masses on different polyhedra
could be different. 相似文献
5.
S. M. El-Shaboury 《Astrophysics and Space Science》1990,174(1):151-154
The restricted problem of three bodies with variable masses is considered. It is assumed that the infinitesimal body is axisymmetric with constant mass and the finite bodies are spherical with variable masses such that the ratio of their masses remains constant. The motion of the finite bodies are determined by the Gyldén-Meshcherskii problem. It is seen that the collinear, triangular, and coplanar solutions not exist, but these solutions exist when the infinitesimal body be a spherical. 相似文献
6.
Rogerio Deienno Diogo Merguizo Sanchez Antonio Fernando Bertachini de Almeida Prado Georgi Smirnov 《Celestial Mechanics and Dynamical Astronomy》2016,124(4):433-456
We analyze the families of central configurations of the spatial 5-body problem with four masses equal to 1 when the fifth mass m varies from 0 to \(+\infty \). In particular we continue numerically, taking m as a parameter, the central configurations (which all are symmetric) of the restricted spatial (\(4+1\))-body problem with four equal masses and \(m=0\) to the spatial 5-body problem with equal masses (i.e. \(m=1\)), and viceversa we continue the symmetric central configurations of the spatial 5-body problem with five equal masses to the restricted (\(4+1\))-body problem with four equal masses. Additionally we continue numerically the symmetric central configurations of the spatial 5-body problem with four equal masses starting with \(m=1\) and ending in \(m=+\infty \), improving the results of Alvarez-Ramírez et al. (Discrete Contin Dyn Syst Ser S 1: 505–518, 2008). We find four bifurcation values of m where the number of central configuration changes. We note that the central configurations of all continued families varying m from 0 to \(+\infty \) are symmetric. 相似文献
7.
A complete solution is given for a symmetric case of the problem of the planar central configurations of four bodies, when two bodies are on an axis of symmetry, and the other two bodies have equal masses and are situated symmetrically with respect to the axis of symmetry. The positions of the bodies on the axis of symmetry are described by angle coordinates with respect to the outside bodies. The solution is such, that giving the angle coordinates, the masses for which the given configuration is a central configuration, can be computed from simple analytical expressions of the angles. The central configurations can be described as one-parameter families, and these are discussed in detail in one convex and two concave cases. The derived formulae represent exact analytical solutions of the four-body problem. 相似文献
8.
Planar central configurations of four different masses are analyzed theoretically and computed numerically. We follow Dziobek’s
approach to four-body central configurations with a straightforward implicit (in the masses and distances) method of our own
in which the fundamental quantities are each the quotient of a directed area divided by the corresponding mass. We apply a
new simple numerical algorithm to construct general four-body central configurations. We use this tool to obtain new properties
of the symmetric and non-symmetric central configurations. The explicit continuous connection between three-body and four-body
central configurations where one of the four masses approaches zero is clarified. Some cases of coorbital 1+3 problems are
also considered. 相似文献
9.
We study planar central configurations of the five-body problem where three of the bodies are collinear, forming an Euler
central configuration of the three-body problem, and the two other bodies together with the collinear configuration are in
the same plane. The problem considered here assumes certain symmetries. From the three bodies in the collinear configuration,
the two bodies at the extremities have equal masses and the third one is at the middle point between the two. The fourth and
fifth bodies are placed in a symmetric way: either with respect to the line containing the three bodies, or with respect to
the middle body in the collinear configuration, or with respect to the perpendicular bisector of the segment containing the
three bodies. The possible stacked five-body central configurations satisfying these types of symmetries are: a rhombus with
four masses at the vertices and a fifth mass in the center, and a trapezoid with four masses at the vertices and a fifth mass
at the midpoint of one of the parallel sides. 相似文献
10.
Esther Barrabés Josep M. Cors Claudio Vidal 《Celestial Mechanics and Dynamical Astronomy》2017,129(1-2):153-176
We outline some aspects of the dynamics of an infinitesimal mass under the Newtonian attraction of three point masses in a symmetric collinear relative equilibria configuration when a repulsive Manev potential (\(-1/r +e/r^{2}\)), \(e>0\), is applied to the central mass. We investigate the relative equilibria of the infinitesimal mass and their linear stability as a function of the mass parameter \(\beta \), the ratio of mass of the central body to the mass of one of two remaining bodies, and e. We also prove the nonexistence of binary collisions between the central body and the infinitesimal mass. 相似文献
11.
Alan Almeida santos 《Celestial Mechanics and Dynamical Astronomy》2004,90(3-4):213-238
We consider some questions on central configurations of five bodies in space. In the first one, we get a general result of
symmetry for the restricted problem of n+1 bodies in dimension n-1. After that, we made the calculation of all c.c. for n=4.
In our second result, we extend a theorem of symmetry due to [Albouy, A. and Libre, I.: 2002, Contemporary Math.
292, 1-16] on non-convex central configurations with 4 unit masses and an infinite central mass. We obtain similar results in
the case of a big, but finite central mass. Finally, we continue the study by [Schmidt, D.S.: 1988, Contemporary Math.
81 ] of the bifurcations of the configuration with four unit masses located at the vertices of a equilateral tetrahedron and
a variable mass at the barycenter. Using Liapunov-Schmidt reduction and a result on bifurcation equations, which appear in
[Golubitsley, M., Stewart, L. and Schaeffer, D.: 1988, Singularties and Groups in Bifurcation Theory, Vol. II, Springer-Verlag, New York], we show that there exist indeed seven families of central configurations close to a
regular tetrahedron parameterized by the value of central mass. 相似文献
12.
The restricted problem of 2 + 2 bodies when one of the infinitesimal masses is further acted upon by the light pressure of the two primaries, is considered. The stationary solutions of this problem are found out. A short discussion is devoted to the stability of these solutions. 相似文献
13.
The concept of central configuration is important in the study of total collisions or the relative equilibrium state of a rotating system in the N-body problem. However, relatively few such configurations are known. Aided by a new global optimizer, we have been able to construct new families of coplanar central configurations having particles of equal mass, and extend these constructions to some configurations with differing masses and the non-coplanar case. Meyer and Schmidt had shown that a theorem of Palmore concerning coplanar central configurations was incorrect for N equal masses where 6 N 20 but presented a simple analytic argument only for N = 6. Using straightforward analytic arguments and inequalities we also disprove this theorem for 2N equal masses with N 3. 相似文献
14.
Josefina Casasayas Jaume Llibre Ana Nunes 《Celestial Mechanics and Dynamical Astronomy》1994,60(2):273-288
In this paper, we give a new derivation of the equations for the central configurations of the 1+n body problem. In the case of equal masses, we show that forn large enough there exists only one solution. Our lower bound forn improves by several orders of magnitude the one previously found by Hall. 相似文献
15.
We strengthen a generic finiteness result due to Moeckel by showing that the number of spatial central configurations of the
Newtonian five-body problem with positive masses is finite, apart from some explicitly given special cases of mass values. 相似文献
16.
In the n-body problem a central configuration is formed if the position vector of each particle with respect to the center
of mass is a common scalar multiple of its acceleration vector. We consider the problem: given a collinear configuration of
four bodies, under what conditions is it possible to choose positive masses which make it central. We know it is always possible
to choose three positive masses such that the given three positions with the masses form a central configuration. However
for an arbitrary configuration of four bodies, it is not always possible to find positive masses forming a central configuration.
In this paper, we establish an expression of four masses depending on the position x and the center of mass u, which gives a central configuration in the collinear four body problem. Specifically we show that there is a compact region
in which no central configuration is possible for positive masses. Conversely, for any configuration in the complement of
the compact region, it is always possible to choose positive masses to make the configuration central. 相似文献
17.
Martha Alvarez-Ramírez Joaquín Delgado 《Celestial Mechanics and Dynamical Astronomy》2003,87(4):371-381
We consider the symmetric planar (3 + 1)-body problem with finite masses m
1 = m
2 = 1, m
3 = µ and one small mass m
4 = . We count the number of central configurations of the restricted case = 0, where the finite masses remain in an equilateral triangle configuration, by means of the bifurcation diagram with as the parameter. The diagram shows a folding bifurcation at a value consistent with that found numerically by Meyer [9] and it is shown that for small > 0 the bifurcation diagram persists, thus leading to an exact count of central configurations and a folding bifurcation for small m
4 > 0. 相似文献
18.
In this paper we have proved the existence of libration points for the generalised photogravitational restricted problem of three bodies. We have assumed the infinitesimal mass of the shape of an oblate spheroid and both of the finite masses to be radiating bodies and the effect of their radiation pressure on the motion of the infinitesimal mass has also been taken into account. It is seen that there is a possibility of nine libration points for small values of oblateness, three collinear, four coplanar and two triangular. 相似文献
19.
We consider the problem: given a collinear configuration of n bodies, find the masses which make it central. We prove that for n ≤ 6, each configuration determines a one-parameter family
of masses (after normalization of the total mass). The parameter is the center of mass when n is even and the square of the angular velocity of the corresponding circular periodic orbit when n is odd. The result is expected to be true for any n.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
20.
Masayoshi Sekiguchi 《Celestial Mechanics and Dynamical Astronomy》2004,90(3-4):355-360
The bifurcation of central configuration in the Newtonian N-body problem for any odd number N ≥ 7 is shown. We study a special
case where 2n particles of mass m on the vertices of two different coplanar and concentric regular n-gons (rosette configuration)
and an additional particle of mass m0 at the center are governed by the gravitational law he 2n+1 body problem. This system is of two degrees of freedom and permits
only one mass parameter μ =m
0/m. This parameter μ controls the bifurcation. If n≥ 3, namely any odd N ≥ 7, then the number of central configurations is three
when μ ≥ μ
c
, and one when μ ≥ μ
c
. By combining the results of the preceding studies and our main theorem, explicit examples of bifurcating central configuration
are obtained for N ≤ 13, for any odd N ∈ [15,943], and for any N ≥ 945. 相似文献