共查询到20条相似文献，搜索用时 31 毫秒
1.
Julian I. Palmore 《Celestial Mechanics and Dynamical Astronomy》1981,25(1):79-80
We elaborate a variational method used recently in the proof of Saari's conjecture.Research supported in part by NSF grant MCS 78-00395. 相似文献
2.
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
3.
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
4.
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
5.
B. Elmabsout 《Celestial Mechanics and Dynamical Astronomy》1990,49(3):219-231
Resumé On démontre dans cet article l'instabilité, pour tout n 4, des configurations d'équilibre relatif dans le problème des n corps, oú les n corps soumises aux attractions newtonniennes mutuelles se trouvent aux sommets d'un polygone régulier de n cotés. La preuve consiste à montrer que les équations aux variations, projetées sur le plan P des n corps, possèdent au moins deux exposants caractéristiques complexes connugués dont la parr'e réelle est strictement positive; alors que ces equations projetées sur un axe orthogonal à P possèdent des solutions ayant des termes séculaires.
We prove in this paper the instability, for all n 4, of the configurations of relative equilibrium in the n-body problem where the n bodies submitted to newtonian mutual attractions are at the vertices of a regular polypon with n sides. For this proof we show that the equations of variations projected to the n bodies plan P have at least two conjugate characteristic exponents with a strictly positive real part; while these equations projected to an orthogonal axis to P have some solutions with secular terms.相似文献
6.
How the Method of Minimization of Action Avoids Singularities 总被引：4，自引：0，他引：4
C. Marchal 《Celestial Mechanics and Dynamical Astronomy》2002,83(1-4):325-353
The method of minimization of action is a powerful technique of proving the existence of particular and interesting solutions of the n-body problem, but it suffers from the possible interference of singularities. The minimization of action is an optimization and, after a short presentation of a few optimization theories, our analysis of interference of singularities will show that:(A) An n-body solution minimizing the action between given boundary conditions has no discontinuity: all n-bodies have a continuous and bounded motion and thus all eventual singularities are collisions;(B) A beautiful extension of Lambert's theorem shows that, for these minimizing solutions, no double collision can occur at an intermediate time;(C) The proof can be extended to triple and to multiple collisions. Thus, the method of minimization of action leads to pure n-body motions without singularity at any intermediate time, even if one or several collisions are imposed at initial and/or final times.This method is suitable for non-infinitesimal masses only. Fortunately, a similar method, with the same general property with respect to the singularities, can be extended to n-body problems including infinitesimal masses. 相似文献
7.
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
8.
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
9.
Wang Qiu-Dong 《Celestial Mechanics and Dynamical Astronomy》1990,50(1):73-88
The problem of finding a global solution for systems in celestial mechanics was proposed by Weierstrass during the last century. More precisely, the goal is to find a solution of the n-body problem in series expansion which is valid for all time. Sundman solved this problem for the case of n = 3 with non-zero angular momentum a long time ago. Unfortunately, it is impossible to directly generalize this beautiful theory to the case of n > 3 or to n = 3 with zero-angular momentum.A new blowing up transformation, which is a modification of McGehee's transformation, is introduced in this paper. By means of this transformation, a complete answer is given for the global solution problem in the case of n > 3 and n = 3 with zero angular momentum.The main result in this paper has appeared in Chinese in Acta Astro. Sinica. 26 (4), 313–322. In this version some mistakes have been rectified and the problems we solved are now expressed in a much clearer fashion. 相似文献
10.
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
11.
Emmanuelle Julliard-Tosel 《Celestial Mechanics and Dynamical Astronomy》2000,76(4):241-281
We give here a proof of Bruns’ Theorem which is both complete and as general as possible:
Generalized Bruns’ Theorem.In the Newtonian (n+1)-body problem in
ℝ
p
with n≥2 and 1≤p≤n+1, every first integral which is algebraic with respect to positions, linear momenta and time, is an algebraic function of the
classical first integrals: the energy, the p(p−1)/2 components of angular momentum and the 2p integrals that come from the uniform linear motion of the center of mass.
Bruns’ Theorem only dealt with the Newtonian three-body problem in ℝ3; we have generalized the proof to n+1 bodies in ℝp with p≤n+1. The whole proof is much more rigorous than the previous versions (Bruns, Painlevé, Forsyth, Whittaker and Hagiara). Poincaré
had picked out a mistake in the proof; we have understood and developed Poincaré’s instructions in order to correct this point
(see Subsection 3.1). We have added a new paragraph on time dependence which fills in an up to now unnoticed mistake (see
Section 6). We also wrote a complete proof of a relation which was wrongly considered as obvious (see Section 3.3). Lastly,
the generalization, obvious in some parts, sometimes needed significant modifications, especially for the case p=1 (see Section 4).
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.
We continue to study the number of isolating integrals in dynamical systems with three and four degrees of freedom, using as models the measure preserving mappingsT already introduced in preceding papers (Froeschlé, 1973; Froeschlé and Scheidecker, 1973a).Thus, we use here a new numerical method which enables us to take as indicator of stochasticity the variation withn of the two (respectively three) largest eigenvalues-in absolute magnitude-of the linear tangential mappingT
n
* ofT
n
. This variation appears to be a very good tool for studying the diffusion process which occurs during the disappearance of the isolating integrals, already shown in a previous paper (Froeschlé, 1971). In the case of systems with three degrees of freedom, we define and give an estimation of the diffusion time, and show that the gambler's ruin model is an approximation of this diffusion process. 相似文献
14.
We consider the non-canonical Hamiltonian dynamics of a gyrostat in Newtonian interaction with n spherical rigid bodies. Using the symmetries of the system we carry out two reductions. Then, working in the reduced problem,
we obtain the equations of motion, a Casimir function of the system and the equations that determine the relative equilibria.
Global conditions for existence of relative equilibria are given. Besides, we give the variational characterization of these
equilibria and three invariant manifolds of the problem; being calculated the equations of motion in these manifolds, which
are described by means of a canonical Hamiltonian system. We give some Eulerian and Lagrangian equilibria for the four body
problem with a gyrostat. Finally, certain classical problems of Celestial Mechanics are generalized. 相似文献
15.
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
16.
Stuart D. Jordan 《Solar physics》1977,51(1):51-59
Calculations performed with several models of the solar chromosphere support Ulmschneider's conclusion that relatively short period acoustic waves heat the low chromosphere in the region just above the temperature minimum. However, these same short period waves (10 period P80 s) are not able to maintain chromospheric temperatures at heights where 5000Å(normal) < 10-6. The calculations also show that an earlier conjecture stating that the H2 population might influence the non-LTE chromospheric H- population is probably not correct, due to lower values of the ratio n
e/n
H inferred from more recent observations. Finally, the calculations support Athay's contention that the Cayrel mechanism alone cannot produce the observed temperature rise, because the magnitude of the radiative cooling in the lines is too great. 相似文献
17.
M. R. Setare 《Astrophysics and Space Science》2010,326(1):27-31
In this paper, we study a cosmological application of the new agegraphic dark energy density in the f(R) gravity framework. We employ the new agegraphic model of dark energy to obtain the equation of state for the new agegraphic
energy density in a spatially flat universe. Our calculations show, taking n<0, that it is possible to have w
Λ crossing −1. This implies that one can generate a phantom-like equation of state from a new agegraphic dark energy model
in a flat universe in the modified gravity cosmology framework. Also, we develop a reconstruction scheme for the modified
gravity with f(R) action. 相似文献
18.
Christopher McCord 《Celestial Mechanics and Dynamical Astronomy》2004,89(2):99-118
In the N-body problem, it is a simple observation that relative equilibria (planar solutions for which the mutual distances between
the particles remain constant) have constant moment of inertia. In 1970, Don Saari conjectured that the converse was true:
if a solution to the N-body problem has constant moment of inertia, then it must be a relative equilibrium. In this note, we confirm the conjecture
for the planar three-body problem with equal masses.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
19.
B andV observations of the suspected variable BV 690 = NSV 04298 are reported. The star shows light variations with a period of
ld.2400 and with amplitudes of 0m.27, 0m.36 and 0m.11 inV, B, andB-V respectively. The light curves show steeper rise than decline, and there is evidence for the presence of a bump in the descending
branch around the phase of 0.35. From considerations of the period, spectral type, presence of the bump and high tangential
velocity we conclude that BV 690 belongs to the BL Herculis class of Typen Cepheids 相似文献
20.
I. Lerche 《Astrophysics and Space Science》1976,41(2):387-406
We give an expression for the radiation produced by a uniformly charged particle when it traverses normally a semi-infinite boundary between two media, both of the same constant; refractive indexn, measured in the appropriate rest frames of the media. The media are taken to slip relative to each other with constant velocity parallel to the boundary.We compute the differential power output and show that (a) the emitted radiation has a flat spectrum up to a frequency such thatn can no longer be considered constant; (b) the angular dependence of the emitted radiation is peaked at an angle to the direction of motion of the particle; (c) there is a back-scattered component to the radiation. in view of the complexity of the analytic formulae for the differential power output we give some numerical examples forn>1 andn<1 to illustrate the different angular dependences of the power output in both cases.Since high energy charged particles are currently thought to be produced in the magnetospheres of pulsars, and since such particles must then escape from the environment of the pulsar by traversing the differentially shearing magnetosphere, it would seem that the simple calculations reported here illustrate a new mechanism for radiation production which is of astrophysical interest. 相似文献