共查询到20条相似文献，搜索用时 31 毫秒
1.
This paper deals with the generalized problem of motion of a system of a finite number of bodies (material points).We suppose here that every point of the system acts on another one with a force (attractive or repulsive) directed along the straight line connecting these two points, and proportional to the product of their masses and a certain function of time, mutual distance and its derivatives of the first and second order (Duboshin, 1970).The laws of forces are different for different pairs of points and, generally speaking, the validity of the third axiom of dynamics (law of action and reaction) is not assumed in advance.With these general assumptions we find the conditions for the laws of the forces under which the problem admits the first integrals, analogous to the classic integrals of the many-body problem with the Newton's law of attraction.It is shown furthermore, that in this generalized problem it is possible to obtain an equation, analogous to the classic equation of Lagrange-Jacobi and deduce the conditions of stability or instability of the system in Lagrange's sense.The results obtained may be applied for the investigation of motion in some isolated stellar systems, where the laws of mechanics may be different from the laws in our solar system. 相似文献
2.
V. T. Kondurar 《Celestial Mechanics and Dynamical Astronomy》1974,10(3):327-344
The present paper is a direct continuation of the paper (Duboshin, 1973) in which was proved the existence of one kind of Lagrange (triangle) and Euler (rectilinear) solutions of the general problem of the motion of three finite rigid bodies assuming different laws of interaction between the elementary particles of the rigid bodies. In particular, Duboshin found that the general problem of three rigid bodies permits such solutions in which the centres of mass of the bodies always form an equilateral triangle or always remain on one straight line, and each body possesses an axial symmetry and a symmetry with respect to the plane of the centres of mass and rotates uniformly around its axis orthogonal to this plane. The conditions for the existence of such solutions have also been found. The results in Duboshin's paper have greatly interested the author of the present paper. In another paper (Kondurar and Shinkarik, 1972) considering a more special problem, when two of the three bodies are spheres, either homogeneous or possessing a spherically symmetric distribution of the densities or of the material points, and the third is an axially symmetrical body possessing equatorial symmetry, the present author obtained analogous solutions of the ‘float’ type describing the motion of the indicated dynamico-symmetrical body in assuming its passive gravitation. In the present paper new Lagrange solutions of the considered general problems of three rigid bodies of ‘level’ type are found when the axes of geometrical and mechanical symmetry of all three bodies always lie in the triangle plane, and the bodies themselves rotate inertially around the symmetry axis, independently of the parameters of the orbital motion of the centres of mass as in the ‘float’ case. The study of particular solutions of the general problem of the translatory-rotary motion of three rigid bodies, which are a generalization of Lagrange solutions, is in the author's opinion, a novelty of some interest for both theoretical and practical divisions of celestial mechanics. For example, in recent times the problem of the libration points of the Earth-Moon system has acquired new interest and value. A possible application which should be mentioned is that to the orbits of artificial satellites near the triangular libration points to serve as observation stations with the aim of specifying the physical parameters in the Earth-Moon system (e.g., the relation of the Earth's mass to the Moon's mass for investigating the orientation of the satellite, solar radiation, etc.). 相似文献
3.
G. N. Doubochine 《Celestial Mechanics and Dynamical Astronomy》1984,33(1):31-47
In the present paper the problem of translatory-rotatory motion of three rigid bodies is discussed. It is shown that this problem admits some particular solutions, when each body possesses axial symetry and the plan of equator. 相似文献
4.
G. N. Duboshin 《Celestial Mechanics and Dynamical Astronomy》1971,4(3-4):423-441
The particular case of the complete generalized three-body problem (Duboshin, 1969, 1970) where one of the body-points does not exert influence on the other two is analysed. These active material points act on the passive point and also on each other with forces (attraction or repulsion), proportional to the product of masses of both points and a certain function of the time, their mutual distances and their first and second derivatives. Furthermore it is not supposed that generally the third axiom of mechanics (action=reaction) takes place.Here under these more general assumptions the equations of motion of the active masses and the passive point, as well as the diverse transformations of these equations are analogous of the same transformations which are made in the classical case of the restricted three-body problem.Then we determine conditions for some particular solutions which exist, when the three points form the equilateral triangle (Lagrangian solutions) or remain always on a straight line (Eulerian solutions).Finally, assuming that some particular solutions of the above kind exist, the character of solutions near this particular one is envisaged. For this purpose the general variational equations are composed and some conclusions on the Liapunov stability in the simplest cases are made. 相似文献
5.
George Bozis 《Astrophysics and Space Science》1976,43(2):355-368
The angular momentum and the energy integral of the planar three-body problem are used to establish regions of the physical space where motion is allowed to take place. Although forbidden regions exist for both negative and positive values of the energy of the system, the known integrals of the motion always allow for at least one of the three bodies to escape. 相似文献
6.
The motion of two mutually attracting triaxial rigid bodies has been considered. Thirty six particular solutions corresponding to the libration points and analogous to the points Spoke, Arrow and Float (Duboshin, 1959) have been found. The stability of these libration points has been discussed in two categories of cases. In the first category, different shapes of the bodies have been taken and in the second category, the mass and the linear dimensions of one of the bodies have been taken small in comparison to the other. 相似文献
7.
In this paper, the problem of the motion of n gyrostats in a central field, with relative momenta
k
r
(k=1, 2, ..., n) functions of the time, is considered.In these conditions, the existence of the linear and angular momentum integrals is established.Moreover, a sufficient condition for the existence of the Jacobi's Integral is given. This study generalizes the results given by Duboshin for n rigid bodies. 相似文献
8.
G. N. Doubochine 《Celestial Mechanics and Dynamical Astronomy》1982,27(3):267-284
In the present paper the problem of translatory-rotatory motion of two rigid bodies is discussed. Author has shown that this problem admits particular solutions, when each body possesses axial symmetry. In these solutions the centre of mass of one body described the circular orbit around the other body and each body keeps the invariable orientation about this orbit. 相似文献
9.
V. N. Shinkin 《Celestial Mechanics and Dynamical Astronomy》1993,55(3):249-259
This paper investigates the stability of the motion in the averaged planar general three-body problem in the case of first-order resonance. The equations of the averaged motion of bodies near the resonance surface is obtained and is analytically integrated by quadratures. The stability of the averaged motion is analytically investigated in relation to the semi-major axes, the eccentricities and the resonance phases. An autonomous second-order equation is obtained for the deviation of semiaxes from the resonance surface. This equation has an energy integral and is analytically integrated by quadratures. The quasi-periodic dependence on time with two-frequency basis of the averaged motion of bodies is found. The basic frequencies are analytically calculated. With the help of the mean functionals calculated along integral curves of the averaged problem the new analytic first integrals are constructed with coefficients periodic in time. The analytic conditions of librations of resonance phases are obtained. 相似文献
10.
John T. Conway 《Monthly notices of the Royal Astronomical Society》2000,316(3):540-554
An analytical method originally applied to the problem of the actuator disc in fluid mechanics has been applied to the closely analogous problem of constructing the classical Newtonian potential and attractions. The method can treat axisymmetric problems and also non-axisymmetric cases where matter is confined within axisymmetric boundaries. The potential and attractions for the generalized thin finite disc can be given in closed form in terms of elliptic integrals and elementary functions. For the general case of matter within an axisymmetric boundary, the potentials and attractions can be evaluated as one-dimensional integrals of albeit complex analytical expressions. These expressions represent the fields induced by matter in an extended region as a distribution of gravitating discs. For certain special cases, such as matter bounded by a circular cylinder and also for matter distributed in a spherical region, closed-form solutions can be given that appear to be new. Some non-axisymmetric results are also given for the thin disc of infinite radial extent. 相似文献
11.
F. A. Abd El-Salam S. E. Abd El-Bar M. Rasem S. Z. Alamri 《Astrophysics and Space Science》2014,350(2):507-515
In the present work, the two body problem using a potential of a continued fractions procedure is reformulated. The equations of motion for two bodies moving under their mutual gravity is constructed. The integrals of motion, angular momentum integral, center of mass integral, total mechanical energy integral are obtained. New orbit equation is obtained. Some special cases are followed directly. Some graphical illustrations are shown. The only included constant of the continued fraction procedure is adjusted so as to represent the so called J 2 perturbation term of the Earth’s potential. 相似文献
12.
The equations of motion of the 2+2 body problem (two interacting particles in the gravitational field of two much more massive primaries m1 and m2 in circular keplerian orbit) have an integral analogous to the Jacobi integral of the circular 2+1 body problem. We show here that with 2+2 bodies this integral does not give rise to Hill stability, i.e. to confinement for all time in a portion of the configuration space not allowing for some close approaches to occur. This is because all the level manifolds are connected and all exchanges of bodies between the regions surroundingm
1,m
2 and infinity do not contradict the conservation of the integral. However, it is worth stressing that some of these exchanges are physically meaningless, because they involve either unlimited extraction of potential energy from the binary formed by the small bodies (without taking into account their physical size) or significant mutual perturbations between the small masses without close approach, a process requiring, for the Sun-Jupiter-two asteroids system, timescales longer than the age of the Solar System. 相似文献
13.
Robert S. Harrington 《Celestial Mechanics and Dynamical Astronomy》1969,1(2):200-209
Two applications of von Zeipel's method to the stellar three-body problem eliminate the short period terms and establish two new integrals of the motion beyond the classical integrals. The remaining time averaged problem with only the second order Hamiltonian has one additional integral and can be solved. The motion with the third order averaged Hamiltonian included is more complex, in that there may be additional resonances, and the additional integral does not exist in all cases. 相似文献
14.
L. G. Luk’yanov 《Astronomy Letters》2005,31(8):563-568
We consider the conservative two-body problem with a constant total mass, but with variable individual masses. The problem is shown to be completely integrable for any mass variation law. The Keplerian motion known for the classical two-body problem with constant masses remains valid for the relative motion of the bodies. The absolute motions of the bodies depend on the center-of-mass motion. Hitherto unknown quadratures that depend on the mass variation law were derived for the integrals of motion of the center of mass. We consider some of the laws that are of interest in studying the motion of close binary stars with mass transfer. 相似文献
15.
In the present paper, the motion of three rigid bodies is considered. With a set of new variables, and the 10 first integrals of the motion, the problem is reduced to a system of order 25 and one quadrature. The plane motions are characterized, and finally, an equation for the existence of central configurations (in particular, Lagrangian and Eulerian solutions) has been found. Besides, the case of three axisymmetric ellipsoids is studied. 相似文献
16.
We present an algorithm to compute the incomplete elliptic integral of a general form. The algorithm efficiently evaluates some linear combinations of incomplete elliptic integrals of all kinds to a high precision. Some numerical examples are given as illustrations. This enables us to numerically calculate the values and the partial derivatives of incomplete elliptic integrals of all kinds, which are essential when dealing with many problems in celestial mechanics, including the analytic solution of the torque-free rotational motion of a rigid body around its barycenter. 相似文献
17.
Binary systems are quite common within the populations of near-Earth asteroids, main-belt asteroids, and Kuiper belt asteroids. The dynamics of binary systems, which can be modeled as the full two-body problem, is a fundamental problem for their evolution and the design of relevant space missions. This paper proposes a new shape-based model for the mutual gravitational potential of binary asteroids, differing from prior approaches such as inertia integrals, spherical harmonics, or symmetric trace-free tensors. One asteroid is modeled as a homogeneous polyhedron, while the other is modeled as an extended rigid body with arbitrary mass distribution. Since the potential of the polyhedron is precisely described in a closed form, the mutual gravitational potential can be formulated as a volume integral over the extended body. By using Taylor expansion, the mutual potential is then derived in terms of inertia integrals of the extended body, derivatives of the polyhedron’s potential, and the relative location and orientation between the two bodies. The gravitational forces and torques acting on the two bodies described in the body-fixed frame of the polyhedron are derived in the form of a second-order expansion. The gravitational model is then used to simulate the evolution of the binary asteroid (66391) 1999 KW4, and compared with previous results in the literature. 相似文献
18.
19.
S. M. Elshaboury 《Astrophysics and Space Science》1991,186(2):245-251
The restricted problem of a tri-axial rigid body and two spherical bodies with variable masses be considered. The general solution of the equations of motion of the tri-axial body be obtained in which the motion of the spherical bodies is determined by the classic nonsteady Gyldén-Meshcherskii problem. 相似文献
20.
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