共查询到20条相似文献，搜索用时 31 毫秒
1.
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
2.
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
3.
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
4.
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
5.
A Counterexample to a Generalized Saari's Conjecture with a Continuum of Central Configurations 总被引：1，自引：1，他引：0
Manuele Santoprete 《Celestial Mechanics and Dynamical Astronomy》2004,89(4):357-364
In this paper we show that in the n-body problem with harmonic potential one can find a continuum of central configurations for n= 3. Moreover we show a counterexample to an interpretation of Jerry Marsden Generalized Saari's conjecture. This will help
to refine our understanding and formulation of the Generalized Saari's conjecture, and in turn it might provide insight in
how to solve the classical Saari's conjecture for n≥ 4.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
6.
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
7.
Gregory Buck 《Celestial Mechanics and Dynamical Astronomy》1991,51(4):305-317
Moulton's Theorem says that given an ordering of masses m 1, ..., m nthere exists a unique collinear central configuration. The theorem allows us to ask the questions: What is the distribution of n equal masses in the collinear central configuration? What is the behavior of the distribution as n → ∞? These questions are due to R. Moekel (personal conversation). Central configurations are found to be attracting fixed points of a flow — a flow we might call an auxiliary flow (in the text it is denoted F(X)), since it has little to do with the equations of motion. This flow is studied in an effort to characterize the mass distribution. Specifically, for a collinear central configuration of n equal masses, a bound is found for the position of the masses furthest from the center of mass. Also some facts concerning the distribution of the inner masses are discovered. 相似文献
8.
Equilibrium Points and Central Configurations for the Lennard-Jones 2- and 3-Body Problems 总被引：1，自引：1，他引：0
Montserrat Corbera Jaume Llibre Ernesto Pérez-Chavela 《Celestial Mechanics and Dynamical Astronomy》2004,89(3):235-266
In this paper we study the relative equilibria and their stability for a system of three point particles moving under the
action of a Lennard-Jones potential. A central configuration is a special position of the particles where the position and
acceleration vectors of each particle are proportional, and the constant of proportionality is the same for all particles.
Since the Lennard-Jones potential depends only on the mutual distances among the particles, it is invariant under rotations.
In a rotating frame the orbits coming from central configurations become equilibrium points, the relative equilibria. Due
to the form of the potential, the relative equilibria depend on the size of the system, that is, depend strongly of the momentum
of inertia I. In this work we characterize the relative equilibria, we find the bifurcation values of I for which the number of relative equilibria is changing, we also analyze the stability of the relative equilibria.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
We consider n bodies (with equal mass m) disposed at the vertices of a regular n-gon and rotating rigidly around an additional mass m
0(at its center) with a constant angular velocity (relative equilibrium). In the present paper, we prove results on the existence
and on the linear stability of equilibrium positions for a zero-mass particle submitted to the gravitational field generated
by the previous system.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
10.
We derive general results on the existence of stationary configurations for N co-orbital satellites with small but otherwise arbitrary masses m
i
, revolving on circular and planar orbits around a massive primary. The existence of stationary configurations depends on
the parity of N. If N is odd, then for any arbitrary angular separation between the satellites, there always exists a set of masses (positive or
negative) which achieves stationarity. However, physically acceptable solutions (m
i
> 0 for all i) restrict this existence to sub-domains of angular separations. If N is even, then for given angular separations of the satellites, there is in general no set of masses which achieves stationarity. The case N=3 is treated completely for small arbitrary satellite masses, giving all the possible solutions and their stability, to within
our approximations. 相似文献
11.
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
12.
Jaume Llibre 《Celestial Mechanics and Dynamical Astronomy》1990,50(1):89-96
Central configurations are critical points of the potential function of the n-body problem restricted to the topological sphere where the moment of inertia is equal to constant. For a given set of positive masses m
1,..., m
n we denote by N(m
1, ..., m
n, k) the number of central configurations' of the n-body problem in k modulus dilatations and rotations. If m
n
1,..., m
n, k) is finite, then we give a bound of N(m
1,..., m
n, k) which only depends of n and k. 相似文献
13.
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
14.
R. F. Arenstorf 《Celestial Mechanics and Dynamical Astronomy》1982,28(1-2):9-15
The number of equivalence classes of central configurations (abbr. c.c.) in the planar 4-body problem with three arbitrary and a fourth small mass is investigated. These c.c. are derived according to their generic origin in the 3-body problem. It is shown that each 3-body collinear c.c. generates exactly 2 non-collinear c.c. (besides 4 collinear ones) of 4 bodies with smallm
40; and that any 3-body equilateral triangle c.c. generates exactly 8 or 9 or 10 (depending onm
1,m
2,m
3) planar 4-body c.c. withm
4=0. Further, every one of these c.c. can be continued uniquely to sufficiently smallm
4>0 except when there are just 9; then exactly one of them is degenerate, and we conjecture that it is not continuable tom
4>0.Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics. 相似文献
15.
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
16.
Kevin D. P. Woerner 《Celestial Mechanics and Dynamical Astronomy》1990,49(4):413-421
A theorem of Palmore's concerning coplanar central configurations of equal mass bodies was shown to be false for all even N 6 by Slaminka and Woerner. Using a variation of that argument I prove that Palmore's Theorem is false for all N 6.Northwestern University 相似文献
17.
The effect of small perturbation in the Coriolis and centrifugal forces on the location of libration point in the ‘Robe (1977)
restricted problem of three bodies’ has been studied. In this problem one body,m
1, is a rigid spherical shell filled with an homogeneous incompressible fluid of densityϱ
1. The second one,m
2, is a mass point outside the shell andm
3 is a small solid sphere of densityϱ
3 supposed to be moving inside the shell subject to the attraction ofm
2 and buoyancy force due to fluidϱ
1. Here we assumem
3 to be an infinitesimal mass and the orbit of the massm
2 to be circular, and we also suppose the densitiesϱ
1, andϱ
3 to be equal. Then there exists an equilibrium point (−μ + (ɛ′μ)/(1 + 2μ), 0, 0). 相似文献
18.
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
19.
In the problem of 2+2 bodies in the Robe’s setup, one of the primaries of mass m*1m^{*}_{1} is a rigid spherical shell filled with a homogeneous incompressible fluid of density ρ
1. The second primary is a mass point m
2 outside the shell. The third and the fourth bodies (of mass m
3 and m
4 respectively) are small solid spheres of density ρ
3 and ρ
4 respectively inside the shell, with the assumption that the mass and the radius of third and fourth body are infinitesimal.
We assume m
2 is describing a circle around m*1m^{*}_{1}. The masses m
3 and m
4 mutually attract each other, do not influence the motion of m*1m^{*}_{1} and m
2 but are influenced by them. We also assume masses m
3 and m
4 are moving in the plane of motion of mass m
2. In the paper, the equations of motion, equilibrium solutions, linear stability of m
3 and m
4 are analyzed. There are four collinear equilibrium solutions for the given system. The collinear equilibrium solutions are
unstable for all values of the mass parameters μ,μ
3,μ
4. There exist an infinite number of non collinear equilibrium solutions each for m
3 and m
4, lying on circles of radii λ,λ′ respectively (if the densities of m
3 and m
4 are different) and the centre at the second primary. These solutions are also unstable for all values of the parameters μ,μ
3,μ
4, φ, φ′. Such a model may be useful to study the motion of submarines due to the attraction of earth and moon. 相似文献
20.
This is a study of the stability of strange dwarfs, superdense stars with a small quark core (M
0core
/M
⨀ < 0.017) and an extended crust consisting of atomic nuclei and a degenerate electron gas where the density may be two orders
of magnitude greater than the maximum density for white dwarfs. For a given equation of state, the mass, total number of baryons,
and radius of strange dwarfs are uniquely determined by the central energy density ρ
c
and the energy density ρ
tr
of the crust at the surface of the quark core. Thus, the entire range of variation of ρ
c
and ρ
tr
must be taken into account in studying the stability of these configurations. This can be done by examining a series of configurations
with a fixed rest mass M
0 (total baryon number) of the quark core and different masses of the crust. In each series, ρ
tr
ranges from the value for white dwarfs to ρ
drip
= 4.3∙1011 g/cm3, at which free neutrons are created in the crust. According to the static criterion for stability, stability is lost in an
individual series when the mass of the strange dwarf reaches a maximum as a function of ρ
tr
.
Translated from Astrofizika, Vol. 52, No. 2, pp. 325–332 (May 2009). 相似文献