共查询到20条相似文献，搜索用时 171 毫秒
1.
Fabian Josef Winterberg Efi Meletlidou 《Celestial Mechanics and Dynamical Astronomy》2004,88(1):37-49
We consider Hill's lunar problem as a perturbation of the integrable two-body problem. For this we avoid the usual normalization in which the angular velocity of the rotating frame of reference is put equal to unity and consider as the perturbation parameter. We first express the Hamiltonian H of Hill's lunar problem in the Delaunay variables. More precisely we deduce the expressions of H along the orbits of the two-body problem. Afterwards with the help of the conserved quantities of the planar two-body problem (energy, angular momentum and Laplace–Runge–Lenz vector) we prove that Hill's lunar problem does not possess a second integral of motion, independent of H, in the sense that there exist no analytic continuation of integrals, which are linear functions of in the rotating two-body problem. In connection with the proof of this main result we give a further restrictive statement to the nonintegrability of Hill's lunar problem. 相似文献
2.
C. Beaugé 《Celestial Mechanics and Dynamical Astronomy》2004,88(1):51-68
In this communication we present an analytical model for the restricted three-body problem, in the case where the perturber is in a parabolic orbit with respect to the central mass. The equations of motion are derived explicitly using the so-called Global Expansion of the disturbing function, and are valid for any eccentricity of the massless body, as well as in the case where both secondary masses have crossing orbits. Integrating the equations of motion over the complete passage of the perturber through the system, we are then able to construct a first-order algebraic mapping for the change in semimajor axis, eccentricity and inclination of the perturbed body.Comparisons with numerical solutions of the exact equations show that the map yields precise results, as long as the minimum distance between both bodies is not too small. Finally, we discuss several possible applications of this model, including the evolution of asteroidal satellites due to background bodies, and simulations of passing stars on extra-solar planets. 相似文献
3.
Albert Bosma 《Celestial Mechanics and Dynamical Astronomy》1998,72(1-2):69-90
In these notes I will briefly summarize our knowledge about the dark matter problem, and emphasize the corresponding dynamical
aspects. This covers a wide area of research, so I have been selective, and have concentrated on the subject of dark matter
in nearby galaxies, in particular spirals.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
4.
5.
The Schwarzschild problem (the two-body problem associated to apotential of the form A/r + B/r3 has been qualitativelyinvestigated in an astrophysical framework, exemplified by two likelysituations: motion of a particle in the photogravitational field ofan oblate, rotating star, or in that of a star which generates aSchwarzschild field. Using McGehee-type transformations, regularizedequations of motion are obtained, and the collision singularity isblown up and replaced by the collision manifold (a torus)pasted on the phase space. The flow on is fullycharacterized. Then, reducing the 4D phase space to dimension 2, theglobal flow in the phase plane is depicted for all possible values ofthe energy and for all combinations of nonzero A and B. Eachphase trajectory is interpreted in terms of physical motion,obtaining in this way a telling geometric and physical picture of themodel. 相似文献
6.
Boris Garfinkel 《Celestial Mechanics and Dynamical Astronomy》1970,2(3):359-359
The Ideal Resonance Problem in its normal form is defined by the Hamiltonian (1) $$F = A (y) + 2B (y) sin^2 x$$ with (2) $$A = 0(1),B = 0(\varepsilon )$$ where ? is a small parameter, andx andy a pair of canonically conjugate variables. A solution to 0(?1/2) has been obtained by Garfinkel (1966) and Jupp (1969). An extension of the solution to 0(?) is now in progress in two papers ([Garfinkel and Williams] and [Hori and Garfinkel]), using the von Zeipel and the Hori-Lie perturbation methods, respectively. In the latter method, the unperturbed motion is that of a simple pendulum. The character of the motion depends on the value of theresonance parameter α, defined by (3) $$\alpha = - A\prime /|4A\prime \prime B\prime |^{1/2} $$ forx=0. We are concerned here withdeep resonance, (4) $$\alpha< \varepsilon ^{ - 1/4} ,$$ where the classical solution with a critical divisor is not admissible. The solution of the perturbed problem would provide a theoretical framework for an attack on a problem of resonance in celestial mechanics, if the latter is reducible to the Ideal form: The process of reduction involves the following steps: (1) the ration 1/n2 of the natural frequencies of the motion generates a sequence. (5) $$n_1 /n_2 \sim \left\{ {Pi/qi} \right\},i = 1, 2 ...$$ of theconvergents of the correspondingcontinued fraction, (2) for a giveni, the class ofresonant terms is defined, and all non-resonant periodic terms are eliminated from the Hamiltonian by a canonical transformation, (3) thedominant resonant term and itscritical argument are calculated, (4) the number of degrees of freedom is reduced by unity by means of a canonical transformation that converts the critical argument into an angular variable of the new Hamiltonian, (5) the resonance parameter α (i) corresponding to the dominant term is then calculated, (6) a search for deep resonant terms is carried out by testing the condition (4) for the function α(i), (7) if there is only one deep resonant term, and if it strongly dominates the remaining periodic terms of the Hamiltonian, the problem is reducible to the Ideal form. 相似文献
7.
We propose the Ptolemaic transformation: a canonical change of variables reducing the Keplerian motion to the form of a perturbed Hamiltonian problem. As a solution of the unperturbed case, the Ptolemaic variables define an intermediary orbit, accurate up to the first power of eccentricity, like in the kinematic model of Claudius Ptolemy. In order to normalize the perturbed Hamiltonian we modify the recurrent Lie series algorithm of HoriuuMersman. The modified algorithm accounts for the loss of a term's order during the evaluation of a Poisson bracket, and thus can be also applied in resonance problems. The normalized Hamiltonian consists of a single Keplerian term; the mean Ptolemaic variables occur to be trivial, linear functions of the Delaunay actions and angles. The generator of the transformation may serve to expand various functions in Poisson series of eccentricity and mean anomaly. 相似文献
8.
Boris Garfinkel 《Celestial Mechanics and Dynamical Astronomy》1975,12(2):203-214
An Extended Resonance Problem is defined by the Hamiltonian, $$F = B(y) + 2\mu ^2 A(y)[\sin x + \lambda (y)]^2 \mu<< 1,\lambda = O(\mu ).$$ It is noted here that the phase-plane trajectories exhibit adouble libration, enclosing two centers, for the initial conditions of motion satisfying the inequality $$1 - |\lambda |< |\alpha |< 1 + |\lambda |,$$ where α is the usualresonance parameter. A first order solution for the case of double libration is constructed here by a generalization of the procedure previously used in solving the Ideal Resonance Problem with λ=0. The solution furnishes a reference orbit for a Perturbed Ideal Problem if a double libration occurs as a result of perturbations. 相似文献
9.
S. B. Faruque 《Celestial Mechanics and Dynamical Astronomy》2003,87(4):353-369
A new analytic expression for the position of the infinitesimal body in the elliptic Sitnikov problem is presented. This solution is valid for small bounded oscillations in cases of moderate primary eccentricities. We first linearize the problem and obtain solution to this Hill's type equation. After that the lowest order nonlinear force is added to the problem. The final solution to the equation with nonlinear force included is obtained through first the use of a Courant and Snyder transformation followed by the Lindstedt–Poincaré perturbation method and again an application of Courant and Snyder transformation. The solution thus obtained is compared with existing solutions, and satisfactory agreement is found. 相似文献
10.
In this article we study for first time the motion of charged particleswith neglected mass under the influence of Lorentz and Coulomb forces offour moving celestial bodies. For this problem we give the equations ofmotion, variational equations and energy integral. Also we give theequilibrium configurations demonstrating an extensive numericalinvestigation of the equilibrium points with comments about theirappearance. 相似文献
11.
Jacques Henrard 《Celestial Mechanics and Dynamical Astronomy》1978,18(2):195-204
It is shown that the appearance of higher order resonances (that produce higher order islands on a surface of section), is not an indication of non-integrability. Examples are given and a method is described for constructing integrable Hamiltonians with higher order resonances. 相似文献
12.
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
13.
Boris Garfinkel 《Celestial Mechanics and Dynamical Astronomy》1972,5(2):189-203
The Ideal Resonance Problem, defined by the HamiltonianF=B(y)+2A (y) sin2
x, 1, has been solved in Garfinkelet al. (1971). There the solution has beenregularized by means of a special function
j
, introduced into the new HamiltonianF, under the tacit assumption thatA anB¨' are of order unity.This assumption, violated in some applications of the theory, is replaced here by the weaker assumption ofnormality, which admits zeros ofA andB inshallow resonance. It is shown here that these zeros generate singularities, which can be suppressed if
j
is suitably redefined.With the modified
j
, and with the assumption of normality, the solution is regularized for all values ofB, B¨', andA. As in the previous paper, the solution isglobal, including asymptotically the classical limit withB as a divisor of O(1).A regularized first-order aloorithm is constructed here as an illustration and a check.Presented at the XXII International Congress of I.A.F., Brussels, Belgium, Sept. 20, 1971. 相似文献
14.
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
15.
The Sitnikov's Problem is a Restricted Three-Body Problem of Celestial Mechanics depending on a parameter, the eccentricity,e. The Hamiltonian,H(z, v, t, e), does not depend ont ife=0 and we have an integrable system; ife is small the KAM Theory proves the existence of invariant rotational curves, IRC. For larger eccentricities, we show that there exist two complementary sequences of intervals of values ofe that accumulate to the maximum admissible value of the eccentricity, 1, and such that, for one of the sequences IRC around a fixed point persist. Moreover, they shrink to the planez=0 ase tends to 1. 相似文献
16.
James A. Klimchuk 《Solar physics》2006,234(1):41-77
The question of what heats the solar corona remains one of the most important problems in astrophysics. Finding a definitive
solution involves a number of challenging steps, beginning with an identification of the energy source and ending with a prediction
of observable quantities that can be compared directly with actual observations. Critical intermediate steps include realistic
modeling of both the energy release process (the conversion of magnetic stress energy or wave energy into heat) and the response
of the plasma to the heating. A variety of difficult issues must be addressed: highly disparate spatial scales, physical connections
between the corona and lower atmosphere, complex microphysics, and variability and dynamics. Nearly all of the coronal heating
mechanisms that have been proposed produce heating that is impulsive from the perspective of elemental magnetic flux strands.
It is this perspective that must be adopted to understand how the plasma responds and radiates. In our opinion, the most promising
explanation offered so far is Parker's idea of nanoflares occurring in magnetic fields that become tangled by turbulent convection.
Exciting new developments include the identification of the “secondary instability” as the likely mechanism of energy release
and the demonstration that impulsive heating in sub-resolution strands can explain certain observed properties of coronal
loops that are otherwise very difficult to understand. Whatever the detailed mechanism of energy release, it is clear that
some form of magnetic reconnection must be occurring at significant altitudes in the corona (above the magnetic carpet), so
that the tangling does not increase indefinitely. This article outlines the key elements of a comprehensive strategy for solving
the coronal heating problem and warns of obstacles that must be overcome along the way. 相似文献
17.
To calculate the dynamics of celestial bodies, we suggest the nonclassic interval algorithm based on taking into account explicitly the limitations of the resolving capacity of instrumental observation facilities. This algorithm is consistent with the correspondence principle (has a classic limit) and is a system of integer mappings of a recurrent type which is free of the effect of the round-off error accumulation. Another feature is its relative simplicity, which allowed us to make the calculations less time-consuming as compared to the classic approach. This algorithm was used to calculate the evolution of the Solar System's planetary orbits over times of about 500 million years. The calculations support the results obtained earlier by classic methods and make it possible to conclude that the suggested interval approach can be adequately applied to the planetary problem under consideration. 相似文献
18.
Periodic Solutions in the Ring Problem 总被引：3，自引：0，他引：3
T.J. Kalvouridis 《Astrophysics and Space Science》1999,266(4):467-494
In this article we investigate the symmetric periodic motions of a particle of negligible mass in a coplanar N-body system
consisting of ν=N-1 peripheral equidistant bodies of equal masses and a central body with a different mass. This system which
we refer to as the ring problem, is a simple model approximating the planar problem of N bodies.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
19.
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
20.
Liam M. Healy 《Celestial Mechanics and Dynamical Astronomy》2000,76(2):79-120
Using the elimination of the parallax followed by the Delaunay normalization, we present a procedure for calculating a normal
form of the main problem (J
2 perturbation only) in satellite theory. This procedure is outlined in such a way that an object-oriented automatic symbolic
manipulator based on a hierarchy of algebras can perform this computation. The Hamiltonian after the Delaunay normalization
is presented to order six explicitly in closed form, that is, in which there is no expansion in the eccentricity. The corresponding
generating function and transformation of coordinates, too lengthy to present here to the same order; the generator is given
through order four.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献