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1.
On the stabilization of the collinear libration points of the restricted circular three-body problem
The possibility of stabilizing the collinear libration points of the circular restricted three-body problem by using an additional jet acceleration (constant in magnitude) is investigated. Three stabilization laws are considered when the jet acceleration is either directed continuously to one of the primariesm
1,m
2 or is parallel to the line joining them. The solution of the problem formulated is based on the method of the driving forces structure analysis created by W. Thomson and P. Tait. It is shown that none of the stabilization laws mentioned ensures the existence of the isolated minimum of changed potential energy, and therefore the secular stability of the collinear libration points is impossible. In the 3rd and 4th paragraphs the possibility of a gyroscopic stabilization of these points is considered. It is shown that the gyroscopic stabilization of the external libration points is possible only when jet acceleration is either directed to the distant mass or is parallel to the line joining the primaries. The necessary and sufficient conditions of the gyroscopic stabilization are given. It is also shown that the internal libration points cannot be stabilized by any of the laws considered. For the Earth-Moon system the numerical data of time-existence of the satellite in the vicinity of the libration point situated near the Moon are given. 相似文献
2.
F. M. El-Sabaa 《Celestial Mechanics and Dynamical Astronomy》1993,55(4):323-330
The equations of motion of a rigid body about a fixed point in a central Newtonian field is reduced to the equation of plane motion under the action of potential and gyroscopic forces, using the isothermal coordinates on the inertia ellipsoid.The construction of periodic solutions near the equilibrium points, by using the Lipaunov theorem of holomorphic integral, is obtained and the necessary and sufficient conditions for the stability of the system are given. 相似文献
3.
F. M. El-Sabaa 《Astrophysics and Space Science》1989,162(2):235-242
The equations of motion of a rigid body about a fixed point in a central Newtonian field is reduced to the equation of plane motion under the action of potential and gyroscopic forces, using the isothermal coordinates on the inertia ellipsoid.The construction of periodic solutions nearby equilibrium points, by using the Liapunov theorem of holomorphic integral are obtained and the necessary and sufficient conditions for the stability of the system are given. 相似文献
4.
Joachim Baumgarte Wolfgang von Grünhagen 《Celestial Mechanics and Dynamical Astronomy》1979,20(2):173-178
This paper shows that for the free symmetric top a formulation of the equations of motion is possible, which is Liapunov stable. The formalism applied is equivalent to the conservative stabilization of the Keplerian problem. The perturbed problem appears in -stable form. This stabilization procedure could be useful in celestial mechanics, if the gyroscopic motion of a satellite is considered and one is interested in the exact position of the angles. 相似文献
5.
H. M. Yehia 《Celestial Mechanics and Dynamical Astronomy》1987,41(1-4):275-288
The general problem of motion of a rigid body about a fixed point under the action of stationary non-symmetric potential and gyroscopic forces is considered. The equations of motion in the Euler-Poisson form are derived. An interpretation is given in terms of charged, magnetized gyrostat moving in a superposition of three classical fields. As an example, the problem of motion of a satellite — gyrostat on a circular orbit with respect to its orbital system is reduced to that of its motion in an inertial system under additional magnetic and Lorentz forces.When the body is completely symmetric about one of its axes passing through the fixed point, the above problem is found to be equivalent to another one, in which the body has three equal moments of inertia and the forces are symmetric around a space axis. The last problem is well-studied and the given analogy reveals a number of integrable cases of the original problem. A transformation is found, which gives from each of these cases a class of integrable cases depending on an arbitrary function. The equations of motion are also reduced to a single equation of the second order. 相似文献
6.
The stability of attitude equilibria relative to gravitational torques for a rigid satellite in a circular orbit has been divided into three inertia regions, the Lagrange region of assured Liapunov stability, the Beletskii-Delp region which is often described as stabilized due to gyroscopic coupling, and an assured instability region. The generalization of these regions to the case of dual-spin or gyrostat satellites whose internal spin momentum is along a principal axis is treated here. The stability boundaries are obtained for all possible equilibrium orientations for such vehicles, and the variations of these boundaries corresponding to changes in the internal momentum magnitude, or to aligning the momentum with a different principal axis, are determined.Alexander von Humboldt Research Fellow at the Institut für Mechanik; on sabbatical leave from Columbia University, New York, U.S.A. 相似文献
7.
A. P. Linnell † 《Monthly notices of the Royal Astronomical Society》2002,332(1):21-28
A new composite model eliminates discrepancies between synthetic spectra for the L2000 model of β Lyrae and spectrophotometric scans and charge-coupled device (CCD) spectra of that binary star. The source of the discrepancies is the use of synthetic spectra from standard model atmospheres to represent the radiation characteristics of the accretion disc rim. Substitution of a composite synthetic spectrum to represent the accretion disc rim eliminates the discrepancies and produces accordance with both scan data, including their temporal variation, and CCD spectra. 相似文献
8.
9.
In this paper, a model is developed for the dynamics of a system of two bodies whose material points are under the influence of a central gravitational force. One of the bodies is assumed to be rigid and spherically symmetric, while the other is assumed to be deformable. To develop a tractable model for the system, the deformable body is modeled using Cohen and Muncaster's theory of a pseudo-rigid body. The resulting model of the system has several of the features, such as angular momentum conservation, exhibited by more restrictive models. We also show how the self-gravitation of the deformable body can be accommodated using appropriate constitutive equations for a force tensor. This enables our model to subsume many existing models of ellipsoidal figures of equilibrium. After the model and its conservations have been discussed, attention is restricted to steady motions of the system. Several results, which generalize recent works on rigid satellites, are established for these motions. For a specific choice of constitutive equations for the pseudo-rigid body, we determine the steady motions with the aid of a numerical continuation method. These results can also be considered as generalizations of earlier works on Roche's ellipsoids of equilibrium. 相似文献
10.
The study of resistive ballooning instabilities in line-tied coronal magnetic fields is extended by including viscosity in the stability analysis. The equations that govern the resistive ballooning instabilities are derived and the effects of parallel and perpendicular viscosity are included using Braginskii's stress tensor. Numerical solutions to these equations are obtained under the rigid wall boundary conditions for arcades with cylindrically-symmetric magnetic fields. It is found that viscosity has a stabilizing effect on the resistive ballooning instabilities with perpendicular viscosity being more important by far than parallel viscosity. The strong stabilizing effect of perpendicular viscosity can lead to complete stabilization for realistic values of the equilibrium quantities.Research Assistant at the Belgian Fund for Scientific Research. 相似文献
11.
Vladimir N. Dvornychenko R. Bruce Gerding 《Celestial Mechanics and Dynamical Astronomy》1977,16(3):263-274
The gyroscopic motion of a spin-stabilized satellite due to gravity gradient torques in a circular orbit has been analyzed to varying degrees in numerous publications. This paper shows that the restriction to a circular orbit is, in fact, not essential and with a slight increase in complexity, noncircular orbits may be treated. More importantly, a uniform regression of the orbital node can also be accounted for. The general results are expressed in closed form using Jacobian elliptic functions. Finally, and this is perhaps most important, certain algebraic integrals of the precession are given which can be used to place limits on the excursions of the spin axis without actually solving for the motion. This allows one to design orientations such that the maximum angle between the orbit normal and spin axis never exceeds a specific amount even though the orbit normal is in precession. 相似文献
12.
13.
We study the influence of gravitational stratification of the solar atmosphere on the stability of coronal magnetic structures. In particular we question whether the (presumably stabilizing) influence of the anchoring of the magnetic field lines in the solar photosphere (line-tying) can be adequately modelled by either rigid wall or flow-through boundary conditions on the coronal perturbations, as is commonly done. Using the ideal MHD model without gravitational effects,inertial line-tying alone cannot lead to afull stabilization, as marginal stability cannot be crossed by including only the rapid density increase at the photospheric interface.We demonstrate, using the (localized) ballooning ordering, that when gravity and the corresponding intrinsically stable stratification of the photosphere is included, the points of marginal stability are no longer independent of the density. The sharp increase in density and associated decrease in pressure scale height at the solar surface leads to a stabilizing effect, which may result in a full transition from unstable to stable modes. Gravitational effects imply that rigid wall conditions represent photospheric field line anchoring better than flow-through conditions for determining the stability or modes of oscillation of a coronal equilibrium. Applying rigid wall conditions gives good approximations for frequencies that are much larger than photospheric time scales when the plasma is stable, and growth rates when the plasma is unstable. At the same time we show however that near marginal stability, even when gravity is included, rigid wall conditions are still violated. 相似文献
14.
We compare the results of a numerical integration of the Euler equations for a rigid Earth model covering a time span of 250 years with Kinoshita's theory for the forced nutations and with a new nutation series by Kinoshita and Souchay. We also present numerical corrections to some of the analytically derived nutation terms. 相似文献
15.
C. V. Vishveshwara 《Journal of Astrophysics and Astronomy》1999,20(3-4):103-120
In this article, we first consider briefly the basic properties of the non-rotating Schwarzschild black hole and the rotating
Kerr black hole Rotational effects are then described in static and stationary spacetimes with arial symmetry by studying
inertial forces, gyroscopic precession and gravi-electromagnetism. The results are applied to the black hole spacetimes. 相似文献
16.
Krzysztof Goździewski 《Celestial Mechanics and Dynamical Astronomy》2003,85(1):79-103
In papers (Godziewski and Maciejewski, 1998a, b, 1999), we investigate unrestricted, planar problem of a dynamically symmetric rigid body and a sphere. Following the original statement of the problem by Kokoriev and Kirpichnikov (1988), we assume that the potential of the rigid body is approximated by the gravitational field of a dumb-bell. The model is described in terms of a 2D Hamiltonian depending on three parameters.In this paper, we investigate the stability of triangular equilibria permissible by the dynamics of the model, under the assumption of low-order resonances. We analyze all resonances of order smaller than four, and we examine the stability with application of theorems by Markeev and Sokolsky. These are the possible following cases: the non-diagonal resonance of the first order with two null characteristic frequencies (unstable); resonances of the first order with one nonzero frequency (diagonal and non-diagonal, stable and unstable); the second-order resonance, which is non-diagonal and stable, and the third-order resonance which is generically unstable, except for three points in the parameters' space, corresponding to stable equilibria.We discuss a perturbed version of Kokoriev and Kirpichnikov model, and we find that if the perturbation is small and depends on the coordinates only, the triangular equilibria persist, except if for the unperturbed equilibria the first-order resonance occurs. We show that the resonances of the order higher than two are also preserved if the perturbation acts. 相似文献
17.
We show that the rotation of coronal holes can be understood in terms of a current-free model of the coronal magnetic field, in which holes are the footpoint locations of open field lines. The coronal field is determined as a function of time by matching its radial component to the photospheric flux distribution, whose evolution is simulated including differential rotation, supergranular diffusion, and meridional flow. We find that ongoing field-line reconnection allows the holes to rotate quasi-rigidly with their outer-coronal extensions, until their boundaries become constrained by the neutral line of the photospheric field as it winds up to form stripes of alternating magnetic polarity. This wind-up may be significantly retarded by a strong axisymmetric field component which forces the neutral line to low latitudes; it is also gradually halted by the cross-latitudinal transport of flux via supergranular diffusion and a poleward bulk flow. We conclude that a strong axisymmetric field component is responsible for the prolonged rigid rotation of large meridional holes during the declining phase of the sunspot cycle, but that diffusion and flow determine the less rigid rotation observed near sunspot maximum, when the holes corotate with their confining polarity stripes. 相似文献
18.
《Chinese Astronomy and Astrophysics》1982,6(1):1-4
I discuss the relation between the internal structure of the Moon and the radial distribution of the moonquake foci. I believe that the important factor conditioning the radial distribution is the fact that the rigidity of the lunar material decreases with increasing depth. Using a two-layer model, solutions of the elasticity equations are found for the cases of a uniform surface load and of a uniform radial body force. The results show that when the inner sphere is less rigid than the outer shell, the maximum sheer stress is located near the boundary of the two components, thus explainning why the moonquakes are mostly deep quakes. The results also suggest that a liquid core exists in the Moon. 相似文献
19.
New series of rigid Earth nutations for the angular momemtum axis, the rotation axis and the figure axis, named RDAN97, are
computed using the torque approach. Besides the classical J2 terms coming from the Moon and the Sun, we also consider several
additional effects: terms coming from J3 and J4 in the case of the Moon, direct and indirect planetary effects, lunar inequality,
J2 tilt, planetary‐tilt, effects of the precession and nutations on the nutations, secular variations of the amplitudes, effects
due to the triaxiality of the Earth, new additional out‐of‐phase terms coming from second order effect and relativistic effects.
Finally, we obtain rigid Earth nutation series of 1529 terms in longitude and 984 terms in obliquity with a truncation level
of 0.1 μ (microarcsecond) and 8 significant digits. The value of the dynamical flattening used in this theory is HD=(C-A)/C=0.0032737674
computed from the initial value pa=50′.2877/yr for the precession rate. These new rigid Earth nutation series are then compared
with the most recent models (Hartmann et al., 1998; Souchay and Kinoshita, 1996, 1997; Bretagnon et al., 1997, 1998. We also
compute a benchmark series (RDNN97) from the numerical ephemerides DE403/LE403 (Standish et al., 1995) in order to test our
model. The comparison between our model (RDAN97) and the benchmark series (RDNN97) shows a maximum difference, in the time
domain, of 69 μas in longitude and 29 μas in obliquity. In the frequency domain, the maximum differences are 6 μas in longitude
and 4 μ as in obliquity which is below the level of precision of the most recent observations (0.2 mas in time domain (temporal
resolution of 1 day) and 0.02 mas in frequency domain).
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
20.
J. Larwood 《Monthly notices of the Royal Astronomical Society》1998,299(2):L32-L36
In this Letter, recent results on the nodal precession of accretion discs in close binaries are applied to the discs in some X-ray binary systems. The ratio between the tidally forced precession period and the binary orbital period is given, as well as the condition required for the rigid precession of gaseous Keplerian discs. Hence the minimum precessional period that may be supported by a fluid Keplerian disc is determined. It is concluded that near-rigid body precession of tilted accretion discs can occur and generally reproduce observationally inferred precession periods, for reasonable system parameters. In particular, long periods in SS 433, Her X-1, LMC X-4 and SMC X-1 can be fitted by the tidal model. It is also found that the precession period that has been tentatively put forward for Cyg X-2 cannot be accommodated by a tidally precessing disc model for any realistic choice of system parameters. 相似文献