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1.
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
2.
Two-integral distribution functions for axisymmetric stellar systems with separable densities 总被引：1，自引：0，他引：1
Zhenglu Jiang Leonid Ossipkov 《Monthly notices of the Royal Astronomical Society》2007,382(4):1971-1981
We show different expressions of distribution functions (DFs) which depend only on the two classical integrals of the energy and the magnitude of the angular momentum with respect to the axis of symmetry for stellar systems with known axisymmetric densities. The density of the system is required to be a product of functions separable in the potential and the radial coordinates, where the functions of the radial coordinate are powers of a sum of a square of the radial coordinate and its unit scale. The even part of the two-integral DF corresponding to this type of density is in turn a sum or an infinite series of products of functions of the energy and of the magnitude of the angular momentum about the axis of symmetry. A similar expression of its odd part can be also obtained under the assumption of the rotation laws. It can be further shown that these expressions are in fact equivalent to those obtained by using Hunter & Qian's contour integral formulae for the system. This method is generally computationally preferable to the contour integral method. Two examples are given to obtain the even and odd parts of their two-integral DFs. One is for the prolate Jaffe model and the other for the prolate Plummer model.
It can be also found that the Hunter–Qian contour integral formulae of the two-integral even DF for axisymmetric systems can be recovered by use of the Laplace–Mellin integral transformation originally developed by Dejonghe. 相似文献
It can be also found that the Hunter–Qian contour integral formulae of the two-integral even DF for axisymmetric systems can be recovered by use of the Laplace–Mellin integral transformation originally developed by Dejonghe. 相似文献
3.
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
4.
Michael E. Hough 《Celestial Mechanics and Dynamical Astronomy》1995,62(3):263-287
A new integration theory is formulated for dynamical systems with two degrees of freedom, in the gravitational field of a rotating system. Four integrals of motion may be determined from complete solutions of a system of three first-order, partial differential equations in three independent variables. The solutions of this system define two integral surfaces with space-time coordinates. These surfaces represent two independent solutions of a second-order kinematic system to which the original fourth-order system has been reduced. An integral curve may be represented as the locus of intersection points of the integral surfaces. The new theory is the theoretical basis for a method of analytic continuation of periodic orbits of the circular restricted problem. 相似文献
5.
G. N. Duboshin 《Celestial Mechanics and Dynamical Astronomy》1972,6(1):27-39
The existence of ten first integrals for the classical problem of the motion of a system of material points, mutually attracting according to Newtonian law, is well known.The existence of the analogous ten first integrals for the more complicated problem of the motion of a system of absolutely rigid bodies, whose elementary particles mutually attract according to the Newtonian law, was established by the author (Duboshin, 1958, 1963, 1968).In his later papers (Duboshin, 1969, 1970), the problem of the motion of a system of material points, attracting each other according to a more general law, was considered and, in particular, it was shown under what conditions the ten first integrals, analogous to the classical integrals, may exist for this problem.In the present paper, the generalized problem of translatory-rotatory motion of rigid bodies, whose elementary particles acting upon each other according to arbitrary laws of forces along the straight line joining them, is discussed.The author has shown that the first integrals for this general problem, analogous to the integrals of the problem of the translatory-rotatory motion of rigid bodies, whose elementary particles acting according to the Newtonian law, exist under certain well known conditions.That is, it has been established that if the third axiom of dynamics (action = reaction) is satisfied, then the integrals of the motion of centre of inertia and the integrals of the moment of momentum exist for this generalized problem.If the third axiom is not satisfied, then the above mentioned integrals do not exist.The third axiom is a necessary but not a sufficient condition for the existence of the tenth integral-the energy integral. The tenth integral always exists if the elementary particles of the bodies acting with a force, depend only on the mutual distances between them. In this case the force function exists for the problem and the energy integral can be expressed in a well known form.The tenth integral may exist for some more general case, without expressing the principle of conservation of energy, but permitting calculation of the kinetic energy, if the configuration of a system is given.The problem, in which the elementary particles acting according to the generalized Veber's law (Tisserand, 1896) has been cited as an example of this more general case. 相似文献
6.
We analyze the stability of periodic solutions for Hill’s double-averaged problem by taking into account a central planet’s oblateness. They are generated by steady-state solutions that are stable in the linear approximation. By numerically calculating the monodromy matrix of variational equations, we plot its trace against the integral of the problem—an averaged perturbing function, for two model systems, [(Sun + Moon)-Earth-satellite] and (Sun-Uranus-satellite). We roughly estimate the ranges of values for the parameters of satellite orbits corresponding to periodic solutions of the evolutionary system that are stable in the linear approximation. 相似文献
7.
Paul E. Nacozy 《Astrophysics and Space Science》1971,14(1):40-51
The numerical integration of systems of differential equations that possess integrals is often approached by using the integrals to reduce the number of degrees of freedom or by using the integrals as a partial check on the resulting solution, retaining the original number of degrees of freedom.Another use of the integrals is presented here. If the integrals have not been used to reduce the system, the solution of a numerical integration may be constrained to remain on the integral surfaces by a method that applies corrections to the solution at each integration step. The corrections are determined by using linearized forms of the integrals in a least-squares procedure.The results of an application of the method to numerical integrations of a gravitational system of 25-bodies are given. It is shown that by using the method to satisfy exactly the integrals of energy, angular momentum, and center of mass, a solution is obtained that is more accurate while using less time of calculation than if the integrals are not satisfied exactly. The relative accuracy is ascertained by forward and backward integrations of both the corrected and uncorrected solutions and by comparison with more accurate integrations using reduced step-sizes. 相似文献
8.
Vadim A. Antonov Faziliddin T. Shamshiev 《Celestial Mechanics and Dynamical Astronomy》1993,56(3):451-469
This paper deals with the plane motion of a star in the gravitational field of a system which is in a steady state and rotates with a constant angular velocity. For these systems a class of potentials permitting a local integral, linear with respect to the velocity components, has been found. The concept of the local integral itself was introduced by one of the authors of the present paper (Antonov, 1981). A detailed model has been constructed. The corresponding domain of the particle motion and the form of the trajectory coils have been determined. The result is compared with the motion in a more realistic potential. 相似文献
9.
The confining curves in the general three-body problem are studied; the role of the integralc 2 h (angular momentum squared times energy) as bifurcation parameter is established in a very simple way by using symmetries and changes of scale. It is well known (Birkhoff, 1927) that the bifurcations of the level manifolds of the classical integrals occur at the Euler-Lagrange relative equilibrium configurations. For small values of the mass ratio ε=m 3/m 2 both the positions of the collinear equilibrium points and thec 2 h integral are expanded in power series of ε. In this way the relationship is found between the confining curves resulting from thec 2 h integral in the general problem, and the zero velocity curves given by the Jacobi integral in the corresponding restricted problem. For small values of ε the singular confining curves in the general and in the restricted problem are very similar, but they do not correspond to each other: the offset of the two bifurcation values is, in the usual, system of units of the restricted problem, about one half of the eccentricity squared of the orbits of the two larger bodies. This allows the definition of an approximate stability criterion, that applies to the systems with small ε, and quantifies the qualitatively well known destabilizing effect of the eccentricity of the binary on the third body. Because of this destabilizing effect the third body cannot be bounded by any topological criterion based on the classical integrals unless its mass is larger than a minimum value. As an example, the three-body systems formed by the Sun, Jupiter and one of the small planets Mercury, Mars, Pluto or anyone of the asteroids are found to be ‘unstable’, i.e. there is no way of proving, with the classical integrals, that they cannot cross the orbit of Jupiter. This can be reliably checked with the approximate stability criterion, that given for the most important three-body subsystems of the Solar System essentially the same information on ‘stability’ as the full computation of thec 2 h integral and of the bifurcation values. 相似文献
10.
I. V. Petrovskaya 《Earth, Moon, and Planets》1996,72(1-3):31-34
The probability of variation of the integrals of the orbit as a result of an encounter was found for a two dimensional system. A method of solution of the Kolmogorov-Feller's equation is obtained using this probability function as a kernel, and it allows us to obtain the distribution of the integrals of the orbit as a function of time. The method is applied to the investigation of the evolution of orbits in the outer cometary cloud under the action of galactic stars. We consider the variations of orbits as a purely discontinuous random process, so we take into account not only distant but also close interactions. 相似文献
11.
T. T. Chia 《Astrophysics and Space Science》1977,46(1):239-246
A definite integral which occurs in radiation theory is shown to be equal in value to another definite integral by evaluating the flux from a spherically symmetrical radiating sphere in two ways. As a corollary, an alternate proof of the invariance of the specific intensity of a ray in empty space along its path is presented.Furthermore, the equality of these two indefinite integrals leads to the conversion of members of a class of indefinite and definite integrals involving arbitrary functions of angle into other integrals. These transformations facilitate the calculation of some of these integrals which arise not only in the theory of radiation, but in other physical situations with spherical or axial symmetry — especially those in which inverse-square laws are involved. 相似文献
12.
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
13.
W.J. Boulton 《Planetary and Space Science》1984,32(3):287-296
The effect of solar radiation pressure on the orbits of cylindrical satellites is considered. The cylinder is assumed to reflect radiation both specularly and diffusely. The resultant forces on a stationary cylindrical satellite are given. The evolution of the satellite's orbit is described for two particular modes of rotation. In both cases the satellites are assumed to be in circular Sun-synchronous orbits. 相似文献
14.
H. M. Yehia 《Celestial Mechanics and Dynamical Astronomy》1987,41(1-4):289-295
The problem of motion of a dynamically symmetric gyrostat acted upon by non-symmetric potential forces admitting a cyclic integral is considered. This problem is brought into equivalence with another one concerning the motion of a similar gyrostat under the action of axisymmetric potential forces. Using this analogy, new integrable cases of each of the two problems are obtained from the known cases of the other. The equations of motion are reduced to a single equation of the second order. 相似文献
15.
A. M. Boichenko 《Astrophysics》2004,47(1):134-142
Observational data on the dynamics of stars in the neighborhood of the sun indicate the existence of a third integral besides the integrals of the angular momentum and energy. The Poincaré integral is proposed as a third integral. The consequences of this assumption are derived and compared with available astrophysical data. 相似文献
16.
Under the Maxwell-Boltzmann approach, the study of nuclear reactions in dense astrophysical plasmas under various cases (such as resonant, non-resonant, modified non-resonant, non-resonant under electron screening, and so on) leads to a class of complicated reaction rate integrals. It is shown that this general class of integrals can be identified with an integral involving the product of twoH-functions. This latter integral is evaluated in this article, and following Buschman (1979), several similar results in the published literature are shown to be incorrect. 相似文献
17.
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
18.
Barnabás Deme Bálint Érdi L. Viktor Tóth 《Celestial Mechanics and Dynamical Astronomy》2018,130(11):73
The fragmentation of interstellar molecular clouds has been investigated with great effort by many authors. In this paper, a simple model is given to describe the dynamics of two fragments moving in a special cylindrical potential. Using a modified version of the restricted three-body problem and the corresponding Jacobian integral, some constraints are given for the motion of the fragments. 相似文献
19.
Pierre Magnenat 《Celestial Mechanics and Dynamical Astronomy》1985,35(4):329-342
Three different numerical techniques are tested to determine the number of integrals of motion in dynamical systems with three degrees of freedom.
- The computation of the whole set of Lyapunov Characteristic Exponents (LCE).
- The triple sections in the configurations space.
- The Stine-Noid box-counting technique.
20.
Mayer's variational problem for a point with a limited mass flow rate is described by differential equations of the fourteenth order, allowing for a few first integrals. By reducing the equations to closed canonical form, these integrals are analyzed from the viewpoint of finding a possible solution to the problem via quadratures on zero, intermediate, and maximum thrust sections. In addition to confirming well-known cases of total integrability, this approach enabled us to establish that the essential difficulty of the solution of the space problem with intermediate thrust is reduced to finding one integral, and the solution of the problem with maximum thrust requires two integrals in involution. It is shown that these integrals can be applied to find particular solutions. 相似文献