共查询到20条相似文献,搜索用时 15 毫秒
1.
We study the existence of invariant tori in a neighbourhood of the collinear equilibrium points of the planar three-body problem. To this end some properties of the normal form of the Hamiltonian reduced to the 4D central manifold are proved. Using this normal form, we show that the nondegeneracy conditions of KAM theorem are satisfied for all positive masses, including the 2:1 resonance case. The evaluation of the conditions is done numerically. 相似文献
2.
Stability in the Full Two-Body Problem 总被引:3,自引:3,他引:0
D. J. Scheeres 《Celestial Mechanics and Dynamical Astronomy》2002,83(1-4):155-169
Stability conditions are established in the problem of two gravitationally interacting rigid bodies, designated here as the full two-body problem. The stability conditions are derived using basic principles from the N-body problem which can be carried over to the full two-body problem. Sufficient conditions for Hill stability and instability, and for stability against impact are derived. The analysis is applicable to binary small-body systems such as have been found recently for asteroids and Kuiper belt objects. 相似文献
3.
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
4.
We discuss the equilibrium solutions of four different types of collinear four-body problems having two pairs of equal masses.
Two of these four-body models are symmetric about the center-of-mass while the other two are non-symmetric. We define two
mass ratios as μ
1 = m
1/M
T and μ
2 = m
2/M
T, where m
1 and m
2 are the two unequal masses and M
T is the total mass of the system. We discuss the existence of continuous family of equilibrium solutions for all the four
types of four-body problems. 相似文献
5.
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
6.
Periodic Orbits of a Collinear Restricted Three-Body Problem 总被引:6,自引:0,他引:6
In this paper we study symmetric periodic orbits of a collinear restricted three-body problem, when the middle mass is the largest one. These symmetric periodic orbits are obtained from analytic continuation of symmetric periodic orbits of two collinear two-body problems. 相似文献
7.
Kenneth R. Meyer 《Celestial Mechanics and Dynamical Astronomy》1998,70(3):159-165
We consider the evolution of the stable and unstable manifolds of an equilibrium point of a Hamiltonian system of two degrees of freedom which depends on a parameter,ν. The eigenvalues of the linearized system are complex for ν < 0 and purely imaginary for ν > 0. Thus for ν < 0 the equilibrium has a two‐dimensional stable manifold and a two‐dimensional unstable manifold, but for ν > 0 these stable and unstable manifolds are gone. We study the system defined by the truncated generic normal form in this situation. One of two things happens depending on the sign of a certain quantity in the normal form expansion. In one case the two families detach as a single invariant manifold and recedes from the equilibrium as ν tends away from 0 through positive values. In the other case the stable and unstable manifold are globally connected for ν < 0 and the whole structure of these manifolds shrinks to the equilibrium as ν → 0 and disappears. These considerations have interesting implications about Strömgren's conjecture in celestial mechanics and the blue sky catastrophe of Devaney. 相似文献
8.
A complement to the the analytical solution given by Damour and Deruelle (D&D) in order to solve the differential equations
that describe the conic-like and rectilinear post-Newtonian two-body problem is presented. We show the geometric relation
between the eccentric and true anomalies for the elliptic-like and hyperbolic-like cases and expressions for their velocities
are obtained. A post-Newtonian version of the Lambert's theorem is shown.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
用上海天文台1.56m望远镜和CCD照相机,观测s=5碎片时,发现了类似彗尾的奇异现象。 相似文献
10.
Karri Muinonen Jenni Virtanen Edward Bowell 《Celestial Mechanics and Dynamical Astronomy》2001,81(1-2):93-101
We introduce new techniques for the computation of the collision probability for Earth-crossing asteroids in the case of short observational arcs and/or small numbers of observations. The techniques rely on the orbital element probability density computed using statistical orbital ranging. We apply the techniques to the Earth-crossing asteroid 1998 OX4with non-vanishing collision probability in numerous close approaches after the year 2012 (inclusive). We study the invariance of the collision probability in transformations between different orbital element sets, and develop a Spearman rank correlation measure for the validity of the linear approximation. We introduce an optimized, fast version of the statistical ranging method. 相似文献
11.
In this paper, an efficient iterative method of arbitrary positive integer order of convergence 2 will be established for the two-body universal initial value problem. The method is of dynamic nature in the sense that, on going from one iterative scheme to the subsequent one, only additional instruction is needed. Moreover, which is the most important, the method does not need any a priori knowledge of the initial guess. A property which avoids the critical situations between divergent to very slow convergent solutions, that may exist in other numerical methods which depend on initial guess. Some applications of the method are also given. 相似文献
12.
卫星与空间碎片碰撞预警的快速算法 总被引:8,自引:0,他引:8
提出了一种空间目标与空间碎片碰撞预警的快速计算方法,该算法不仅计算速度快,而且减缓了沿迹误差的影响,延长了预警的有效期,利用该方法,检测一个卫星与5800个空间碎片在一天内是否碰撞,计算时间小于3秒;用2天前的资料,预报计算法国CERISE卫星和空间碎片的碰撞时间误差约为0.02秒,空间位置误差约为500—600米. 相似文献
13.
Mercè Ollé Joan R. Pacha Jordi Villanueva 《Celestial Mechanics and Dynamical Astronomy》2004,90(1-2):87-107
The paper deals with different kinds of invariant motions (periodic orbits, 2D and 3D invariant tori and invariant manifolds of periodic orbits) in order to analyze the Hamiltonian direct Hopf bifurcation that
takes place close to the Lyapunov vertical family of periodic orbits of the triangular equilibrium point L4 in the 3D restricted three-body problem (RTBP) for the mass parameter, μ greater than (and close to) μR (Routh’s mass parameter). Consequences of such bifurcation, concerning the confinement of the motion close to the hyperbolic
orbits and the 3D nearby tori are also described. 相似文献
14.
15.
Kiyotaka Tanikawa 《Celestial Mechanics and Dynamical Astronomy》2000,76(3):157-185
A numerical procedure to systematically find collision orbits in the planar three-body problem has been developed in the preceding
paper (Tanikawa et al., 1995). Using this procedure, a search for binary and triple collision orbits has been carried out
in the free-fall three-body problem. Some detailed structures of a part of the initial value space are discussed. Various
interesting orbits have been found. Examples are oscillatory orbits in which ejected particles change from ejection to ejection,
and orbits which are not isosceles initially but nearly isosceles after escape. Some results of isosceles problems (Simó and
Martínez, 1988) are extended to non-isosceles problems.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
16.
V. S. Kalantonis C. N. Douskos E. A. Perdios 《Celestial Mechanics and Dynamical Astronomy》2006,94(2):135-153
Asymptotic motion to collinear equilibrium points of the restricted three-body problem with oblateness is considered. In particular,
homoclinic and heteroclinic solutions to these points are computed. These solutions depart asymptotically from an equilibrium
point and arrive asymptotically at the same or another equilibrium point and are important reference solutions. To compute
an asymptotic orbit, we use a fourth order local analysis, numerical integration and standard differential corrections. 相似文献
17.
Colin R. Mcinnes 《Celestial Mechanics and Dynamical Astronomy》1997,67(2):167-180
The two-body problem is considered with an additional thrust induced acceleration. Stationary solutions are obtained to this
problem in a rotating frame of reference which generates families of displaced circular orbits when viewed from an internal
frame of reference. The existence and stability of these orbits is considered along with applications such as in-situ observations
of Saturn's ring system and spacecraft proximity operations.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
18.
Sergey Bolotin 《Celestial Mechanics and Dynamical Astronomy》2005,93(1-4):343-371
We consider the plane restricted elliptic 3 body problem with small mass ratio and small eccentricity and prove the existence
of many periodic orbits shadowing chains of collision orbits of the Kepler problem. Such periodic orbits were first studied
by Poincaré for the non-restricted 3 body problem. Poincaré called them second species solutions. 相似文献
19.
20.
T. G. Vozmischeva 《Celestial Mechanics and Dynamical Astronomy》2000,77(1):37-48
The generalization of a test particle motion in a central field of two immovable point-like centers to the case of a constant
curvature space, on a three-dimensional sphere, is investigated in the paper. The bifurcation set in the plane of integrals
of motion is constructed and the classification of the domains of possible motion is carried out on a two-dimensional sphere.
The regularization of the Kepler’s problem on a two-dimensional sphere is carried out.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献