共查询到20条相似文献，搜索用时 31 毫秒
1.
Using the famous Sundman inequality, we have constructed for the first time the surfaces for the general three-body problem that we suggest calling Sundman surfaces. These surfaces are a generalization of the widely known Hill surfaces in the restricted circular three-body problem. The Sundman surfaces are constructed in a rectangular coordinate system that uses the mutual distances between the bodies as the Cartesian rectangular coordinates. The singular points of the family of these surfaces have been determined. The possible and impossible regions of motion of the bodies have been constructed in the space of mutual distances. We have shown the existence of Hill stable motions and established sufficient criteria for Hill stability of motions. Some of the astronomical applications are considered. 相似文献
2.
Abdullah A. Ansari Ziyad Ali Alhussain Sada Nand Prasad 《Journal of Astrophysics and Astronomy》2018,39(5):57
The circular restricted three-body problem, where two primaries are taken as heterogeneous oblate spheroid with three layers of different densities and infinitesimal body varies its mass according to the Jeans law, has been studied. The system of equations of motion have been evaluated by using the Jeans law and hence the Jacobi integral has been determined. With the help of system of equations of motion, we have plotted the equilibrium points in different planes (in-plane and out-of planes), zero velocity curves, regions of possible motion, surfaces (zero-velocity surfaces with projections and Poincaré surfaces of section) and the basins of convergence with the variation of mass parameter. Finally, we have examined the stability of the equilibrium points with the help of Meshcherskii space–time inverse transformation of the above said model and revealed that all the equilibrium points are unstable. 相似文献
3.
S. A. Gasanov 《Astronomy Letters》2008,34(3):179-188
We have found libration points and investigated their Lyapunov stability in the problem of the motion of a star inside a layered inhomogeneous rotating elliptical galaxy with a variable mass. We have constructed the surfaces of zero velocity and obtained stability conditions for unsteady motion in the first approximation. We analyze general case where the densities of the galactic nucleus and layers vary with time according to different laws. 相似文献
4.
Giovanni B. Valsecchi Andrea Carusi Archie E. Roy 《Celestial Mechanics and Dynamical Astronomy》1984,32(3):217-230
Hill-type stability surfaces are computed for the general hierarchical three-body problem for non-zero eccentricities of the initial osculating orbits. Significant differences are found between them and the one obtained for initial zero eccentricities. Application is made to the triple subgroups of the Solar System; in particular it is found that no analytical guarantee of Hill-type stability can be given to any of the satellites against solar perturbations. 相似文献
5.
S. A. Elwakil E. A. Saad M. T. Attia S. K. El-Labany 《Astrophysics and Space Science》1989,161(1):35-45
The problem of heat flux at the critical surfaces and the surfaces of a pellet of deuterium and tritium (conduction zone) heated by laser have been considered. Ion-electron collisions are only allowed for: i.e., the linear transport equation is used to describe the problem with boundary conditions consists of isotropic and diffuse boundary conditions. The bi-variational technique has been used to calculate the electron density and temperature across the conduction zone as well as the heat flux. Numerical results are given and compared with those of Rouse and Williams (1981) results. 相似文献
6.
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
7.
8.
One- and two-dimensional sections of the region of initial conditions in the vicinity of a periodic Ducati orbit have been studied in detail in the plane equal-mass three-body problem. A continuous stability region generated by the periodic Ducati orbit has been revealed. In addition, a number of other stability regions that are probably related to stable hierarchical triple systems have been found. Several specific trajectories from the stability regions and in the boundary zones are analyzed. 相似文献
9.
10.
The nonlinear stability of triangular equilibrium points has been discussed in the generalised photogravitational restricted
three body problem with Poynting-Robertson drag. The problem is generalised in the sense that smaller primary is supposed
to be an oblate spheroid. The bigger primary is considered as radiating. We have performed first and second order normalization
of the Hamiltonian of the problem. We have applied KAM theorem to examine the condition of non-linear stability. We have found
three critical mass ratios. Finally we conclude that triangular points are stable in the nonlinear sense except three critical
mass ratios at which KAM theorem fails. 相似文献
11.
R. A. Broucke 《Celestial Mechanics and Dynamical Astronomy》1994,58(2):99-123
We describe a collection of results obtained by numerical integration of orbits in the main problem of artificial satellite theory (theJ
2 problem). The periodic orbits have been classified according to their stability and the Poincaré surfaces of section computed for different values ofJ
2 andH (whereH is thez-component of angular momentum). The problem was scaled down to a fixed value (–1/2) of the energy constant. It is found that the pseudo-circular periodic solution plays a fundamental role. They are the equivalent of the Poincaré first-kind solutions in the three-body problem. The integration of the variational equations shows that these pseudo-circular solutions are stable, except in a very narrow band near the critical inclincation. This results in a sequence of bifurcations near the critical inclination, refining therefore some known results on the critical inclination, for instance by Izsak (1963), Jupp (1975, 1980) and Cushman (1983). We also verify that the double pitchfork bifurcation around the critical inclination exists for large values ofJ
2, as large as |J
2|=0.2. Other secondary (higher-order) bifurcations are also described. The equations of motion were integrated in rotating meridian coordinates. 相似文献
12.
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
13.
Zdeněk Kopal 《Astrophysics and Space Science》1987,134(1):55-71
The aim of the present paper will be to extend the methods of our previous investigations (Kopal, 1980, 1987) by employing the Clairaut coordinates (in which the radial component is identified with the total potential) to analyze the nature of small oscillations about the equilibrium form of Roche double-star model (identical, in fact, with zero-velocity surfaces of the restricted problem of three bodies).Linearized equations of this problem have been set up in Clairaut coordinates, and solved in a closed form. This solution turns out to be closely analogous to that obtained already for the rotating single-star Roche model, and discloses that (like in the preceding case) the terms secular in time appear already in the linear approximation. However, whether or not a retention of nonlinear terms in the equations of motion can regain secular stability of the respective configurations remains yet to be clarified by future investigations. 相似文献
14.
Yu. S. Osipov 《Celestial Mechanics and Dynamical Astronomy》1977,16(2):191-208
The main result of this paper is a theorem on the trajectory equivalence of phase flows on isoenergetic surfaces with a positive energy level in the Kepler problem and perturbed kepler problem. The following two facts are crucial for proving it: firstly, an isomorphism of the phase flow on an isoenergetic surface in the Kepler problem and the geodesic flow in a constant curvature space. The isomorphism is studied in detail. In particular, all the integrals of the Kepler problem are obtained proceeding from the group-theory considerations. The second fact is a generalization of the theorem on structural stability of Anosov flows onto non-compact manifolds. 相似文献
15.
The motion of a point mass in the J 2 problem is generalized to that of a rigid body in a J 2 gravity field. The linear and nonlinear stability of the classical type of relative equilibria of the rigid body, which have been obtained in our previous paper, are studied in the framework of geometric mechanics with the second-order gravitational potential. Non-canonical Hamiltonian structure of the problem, i.e., Poisson tensor, Casimir functions and equations of motion, are obtained through a Poisson reduction process by means of the symmetry of the problem. The linear system matrix at the relative equilibria is given through the multiplication of the Poisson tensor and Hessian matrix of the variational Lagrangian. Based on the characteristic equation of the linear system matrix, the conditions of linear stability of the relative equilibria are obtained. The conditions of nonlinear stability of the relative equilibria are derived with the energy-Casimir method through the projected Hessian matrix of the variational Lagrangian. With the stability conditions obtained, both the linear and nonlinear stability of the relative equilibria are investigated in details in a wide range of the parameters of the gravity field and the rigid body. We find that both the zonal harmonic J 2 and the characteristic dimension of the rigid body have significant effects on the linear and nonlinear stability. Similar to the classical attitude stability in a central gravity field, the linear stability region is also consisted of two regions that are analogues of the Lagrange region and the DeBra-Delp region respectively. The nonlinear stability region is the subset of the linear stability region in the first quadrant that is the analogue of the Lagrange region. Our results are very useful for the studies on the motion of natural satellites in our solar system. 相似文献
16.
To illustrate his theory of coronal heating, Parker initially considers the problem of disturbing a homogeneous vertical magnetic
field that is line-tied across two infinite horizontal surfaces. It is argued that, in the absence of resistive effects, any
perturbed equilibrium must be independent of z. As a result random footpoint perturbations give rise to magnetic singularities, which generate strong Ohmic heating in the
case of resistive plasmas. More recently these ideas have been formalized in terms of a magneto-static theorem but no formal
proof has been provided. In this paper we investigate the Parker hypothesis by formulating the problem in terms of the fluid
displacement. We find that, contrary to Parker's assertion, well-defined solutions for arbitrary compressibility can be constructed
which possess non-trivial z-dependence. In particular, an analytic treatment shows that small-amplitude Fourier disturbances violate the symmetry ∂z = 0 for both compact and non-compact regions of the (x, y) plane. Magnetic relaxation experiments at various levels of gas pressure confirm the existence and stability of the Fourier
mode solutions. More general footpoint displacements that include appreciable shear and twist are also shown to relax to well-defined
non-singular equilibria. The implications for Parker's theory of coronal heating are discussed. 相似文献
17.
B. Ishwar 《Celestial Mechanics and Dynamical Astronomy》1996,65(3):253-289
The non-linear stability of the triangular equilibrium point L
4 in the generalized restricted three-body problem has been examined. The problem is generalized in the sense that the infinitesimal body and one of the primaries have been taken as oblate spheroids. It is found that the triangular equilibrium point is stable in the range of linear stability except for three mass ratios. 相似文献
18.
19.
A Riemann ellipsoid is a self-gravitating fluid whose velocity field is a linear function of the position coordinates. Though the theory of the equilibrium and stability is thoroughly developed, scarse attention has been paid to the dynamical behaviour.In this paper we present a numerical exploration of the phase-space structure for the Self-Adjoint S-Type Riemann ellipsoids via Poincaré surfaces of section, which reveal a rich and complex dynamical behaviour.Both the occurrence of chaos for certain values of the parameters of the system as well as the existence of periodic orbits are observed.We also considered ellipsoids embedded in rigid, homogeneous, spherical halos, obtaining evidence of the stabilizing effect of halos even in the case of finite-amplitude oscillations.Moreover, we show that the approximated equations of motion derived by Rosensteel and Tran (1991) fail to describe properly the phase-space structure of the problem. 相似文献
20.
GEORGE BAKER 《Meteoritics & planetary science》1967,3(4):179-217
Abstract. Complete and nearly complete australite buttons in good states of preservation from Port Campbell, Victoria, show excellent structural details and are of great scientific importance. Some of the features on their posterior surfaces are doubtfully assigned a primary origin in an extraterrestrial birthplace but have been modified by terrestrial solution-etching. Secondary features on their anterior surfaces are due to the effects of aerodynamic frictional heating during transit with stable orientation at supersonic velocity through the earth's atmosphere. Tertiary processes such as subaerial weathering have played some part in slightly modifying their shape and sculpture patterns. They contrast strongly with the many thousands of australites collected from the arid and sub-arid regions of Australia, and with a considerable number that were abraded by stream or gravity transportation in the more temperate zones of the strewnfield. The majority of such specimens have been more severely weathered with the resultant loss of much or all of their primary and secondary features. 相似文献