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.
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
3.
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
4.
In this paper we find a class of new degenerate central configurations and bifurcations in the Newtonian n-body problem. In particular we analyze the Rosette central configurations, namely a coplanar configuration where n particles of mass m1 lie at the vertices of a regular n-gon, n particles of mass m2 lie at the vertices of another n-gon concentric with the first, but rotated of an angle π /n, and an additional particle of mass m0 lies at the center of mass of the system. This system admits two mass parameters μ = m0/m1 and ε = m2/m1. We show that, as μ varies, if n > 3, there is a degenerate central configuration and a bifurcation for every ε > 0, while if n = 3 there is a bifurcation only for some values of ε. 相似文献
5.
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
6.
Mercedes Arribas Antonio Elipe Tilemahos Kalvouridis Manuel Palacios 《Celestial Mechanics and Dynamical Astronomy》2007,99(1):1-12
We prove that for generalized forces which are function of the mutual distance, the ring n + 1 configuration is a central configuration. Besides, we show that it is a homographic solution. We apply the above results
to quasi-homogeneous potentials. 相似文献
7.
Josep Maria Cors César Castilho Claudio Vidal 《Celestial Mechanics and Dynamical Astronomy》2009,103(2):163-177
We consider a restricted three-body problem consisting of two positive equal masses m
1 = m
2 moving, under the mutual gravitational attraction, in a collision orbit and a third infinitesimal mass m
3 moving in the plane P perpendicular to the line joining m
1 and m
2. The plane P is assumed to pass through the center of mass of m
1 and m
2. Since the motion of m
1 and m
2 is not affected by m
3, from the symmetry of the configuration it is clear that m
3 remains in the plane P and the three masses are at the vertices of an isosceles triangle for all time. The restricted planar isosceles three-body
problem describes the motion of m
3 when its angular momentum is different from zero and the motion of m
1 and m
2 is not periodic. Our main result is the characterization of the global flow of this problem. 相似文献
8.
We consider the problem of 4 bodies of equal masses in R
3 for the Newtonian r−1 potential. We address the question of the absolute minima of the action integral among (anti)symmetric loops of class H
1 whose period is fixed. It is the simplest case for which the results of [4] (corrected in [5]) do not apply: the minima cannot
be the relative equilibria whose configuration is an absolute minimum of the potential among the configurations having a given
moment of inertia with respect to their center of mass. This is because the regular tetrahedron cannot have a relative equilibrium
motion in R
3 (see [2]). We show that the absolute minima of the action are not homographic motions. We also show that if we force the
configuration to admit a certain type of symmetry of order 4, the absolute minimum is a collisionless orbit whose configuration
‘hesitates’ between the central configuration of the square and the one of the tetrahedron. We call these orbits ‘hip-hop’.
A similar result holds in case of a symmetry of order 3 where the central configuration of the equilateral triangle with a
body at the center of mass replaces the square.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
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
10.
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
11.
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
12.
Angelo B. Mingarelli Chiara M. F. Mingarelli 《Celestial Mechanics and Dynamical Astronomy》2005,91(3-4):391-401
In an effort to understand the nature of almost periodic orbits in the n-body problem (for all time t) we look first to the more basic question of the oscillatory nature of solutions of this problem (on a half-line, usually
taken as R
+). Intimately related to this is the notion of a conjugate point(due to A. Wintner) of a solution. Specifically, by rewriting the mass unrestricted general problem of n-bodies in a symmetric form we prove that in the gravitational Newtonian n-body problem with collisionless motions there exists arbitrarily large conjugate points in the case of arbitrary (positive)
masses whenever the cube of the reciprocal of at least one of the mutual distances is not integrable at infinity. The implication
of this result is that there are possibly many Wintner oscillatorysolutions in these cases (some of which may or may not be almost periodic). As a consequence, we obtain sufficient conditions
for all continuable solutions (to infinity) to be either unbounded or to allow for near misses (at infinity). The results
also apply to potentials other than Newtonian ones. Our techniques are drawn from results in systems oscillation theory and
are applicable to more general situations.
Dedicated to the memory of Robert M. (Bob) Kauffman, formerly Professor of the
University of Alabama in Birmingham 相似文献
13.
An appropriate generalization of the Jacobi equation of motion for the polar moment of inertia I is considered in order to study the N-body problem with variable masses. Two coupled ordinary differential equations governing the evolution of I and the total energy E are obtained. A regularization scheme for this system of differential equations is provided. We compute some illustrative
numerical examples, and discuss an average method for obtaining approximate analytical solutions to this pair of equations.
For a particular law of mass loss we also obtain exact analytical solutions. The application of these ideas to other kind
of perturbed gravitational N-body systems involving drag forces or a different type of mass variation is also considered.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
14.
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
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.
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
17.
Masaya Masayoshi Saito Kiyotaka Tanikawa 《Celestial Mechanics and Dynamical Astronomy》2009,103(3):191-207
We study the change of phase space structure of the rectilinear three-body problem when the mass combination is changed. Generally,
periodic orbits bifurcate from the stable Schubart periodic orbit and move radially outward. Among these periodic orbits there
are dominant periodic orbits having rotation number (n − 2)/n with n ≥ 3. We find that the number of dominant periodic orbits is two when n is odd and four when n is even. Dominant periodic orbits have large stable regions in and out of the stability region of the Schubart orbit (Schubart
region), and so they determine the size of the Schubart region and influence the structure of the Poincaré section out of
the Schubart region. Indeed, with the movement of the dominant periodic orbits, part of complicated structure of the Poincaré
section follows these orbits. We find stable periodic orbits which do not bifurcate from the Schubart orbit. 相似文献
18.
Manuele Santoprete 《Celestial Mechanics and Dynamical Astronomy》2006,94(1):17-35
In this paper, we study the linear stability of the relative equilibria for homogeneous and quasihomogeneous potentials. First,
in the case the potential is a homogeneous function of degree −a, we find that any relative equilibrium of the n-body problem with a>2 is spectrally unstable. We also find a similar condition in the quasihomogeneous case. Then we consider the case of three
bodies and we study the stability of the equilateral triangle relative equilibria. In the case of homogeneous potentials we
recover the classical result obtained by Routh in a simpler way. In the case of quasihomogeneous potentials we find a generalization
of Routh inequality and we show that, for certain values of the masses, the stability of the relative equilibria depends on
the size of the configuration. 相似文献
19.
We have two mass points of equal masses m
1=m
2 > 0 moving under Newton’s law of attraction in a non-collision parabolic orbit while their center of mass is at rest. We
consider a third mass point, of mass m
3=0, moving on the straight line L perpendicular to the plane of motion of the first two mass points and passing through their
center of mass. Since m
3=0, the motion of m
1 and m
2 is not affected by the third and from the symmetry of the motion it is clear that m
3 will remain on the line L. The parabolic restricted three-body problem describes the motion of m
3. Our main result is the characterization of the global flow of this problem. 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