共查询到20条相似文献，搜索用时 15 毫秒
1.
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
2.
F. M. F. El-Sabaa 《Astrophysics and Space Science》1992,193(2):309-315
The equation of motion of a rigid body in the Kovalevskaya case is reduced to a plane motion. By using the method of small parameters introduced by Poincaré the existence of a periodic solution is established. 相似文献
3.
F. M. F. El-Sabaa 《Celestial Mechanics and Dynamical Astronomy》1985,37(1):71-79
The equation of motion of a rigid body in Kovaleveskaya case is reduced to a plane motion. By using the method of small parameters introduced by Poincaré, the existence of a periodic solution is established. 相似文献
4.
V. A. Shefer 《Solar System Research》2005,39(3):239-246
The motion of minor Solar System bodies having close encounters with major planets is described using the model of motion within the framework of the perturbed restricted three-body problem. The actual motion of a minor body is represented as a combination of two motions, namely, the motion of a fictitious attracting center with a variable mass and the motion with respect to the fictitious center. The position and mass of the fictitious center are chosen so that, when the minor body collides with any of the primaries, the fictitious center carries into the center of inertia of the colliding body and the mass of the fictitious center becomes identical to the mass of this body. The regularizing KS-transformation and Sundman’s time transformation were applied to coordinates and velocities. As a result, a system of differential equations of motion that are quasilinear within the nearest vicinity of each of the primary attracting bodies was obtained. These equations are characterized by a numerical behavior during the encounters of the minor body with the primaries that is essentially better than that of the initial equations of motion. The motion of comets Brooks 2 and Gehrels 3, which have fairly close encounters with Jupiter, is simulated.__________Translated from Astronomicheskii Vestnik, Vol. 39, No. 3, 2005, pp. 272–280.Original Russian Text Copyright © 2005 by Shefer. 相似文献
5.
Stability of Surface Motion on a Rotating Ellipsoid 总被引：2，自引：0，他引：2
The dynamical environment on the surface of a rotating, massive ellipsoid is studied, with applications to surface motion on an asteroid. The analysis is performed using a combination of classical dynamics and geometrical analysis. Due to the small sizes of most asteroids, their shapes tend to differ from the classical spheroids found for the planets. The tri-axial ellipsoid model provides a non-trivial approximation of the gravitational potential of an asteroid and is amenable to analytical computation. Using this model, we study some properties of motion on the surface of an asteroid. We find all the equilibrium points on the surface of a rotating ellipsoid and we show that the stability of these points is intimately tied to the conditions for a Jacobi or MacLaurin ellipsoid of equilibria. Using geometrical analysis we can define global constraints on motion as a function of shape, rotation rate, and density, we find that some asteroids should have accumulation of material at their ends, while others should have accumulation of surface material at their poles. This study has implications for motion of a rover on an asteroid, and for the distribution of natural material on asteroids, and for a spacecraft hovering over an asteroid. 相似文献
6.
The collapse, bounce, shock wave and expansion of the envelope of a rotating star have been analysed in the adiabatic approximation using the particle-in-cell method. The bounce takes place first in the equatorial plane and a shock wave arises there which shortly afterwards crosses the surface of the star. In the envelope, and to a less extent in the remainder of the star, there is a fast and lasting meridional motion the direction of which changes. As a consequence of the fast meridional motion in the envelope, mass and angular momentum are transported towards the axis of rotation. If the initial star rotates fast enough this will cause a secondary radial expansion in the polar region and a mass ejection. These motions reduce the strong anisotropy caused originally by the equatorial expansion. Strong whirls may arise along the axis of rotation. In the remainder of the star the meridional motion becomes supersonic. The temperature in the envelope depends to a high degree on the choice of the equation of state. Massloss is proportional to the energy initially added. The final loss of angular momentum and of energy is quite large, both losses being about 25%. 相似文献
7.
S. A. Gasanov 《Astronomy Letters》2007,33(12):827-843
The problem of the motion of a star inside a layered inhomogeneous rotating elliptical galaxy with a variable mass is considered. We have found an analogue of the Jacobi integral and determined the possible regions of motion. A solution to the equations of perturbed motion has been obtained. 相似文献
8.
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
9.
M. A. Vashkov’yak 《Solar System Research》2018,52(4):359-370
The well-known problem of motion in a central field integrable in quadratures is considered. The force function of the problem depends only on the particle distance to the chosen coordinate origin. In the general case of an arbitrary central force, a rigorous analytical solution of the problem cannot be obtained due to the complexity of the integrals. In this paper we propose a semi-analytical method of constructing an approximate solution for the case where the distance varies in a limited range that allows the time dependences of the polar coordinates to be obtained using elliptic functions and integrals. As an example, we consider the model problems of the perturbed motion of hypothetical Jovian and lunar equatorial satellites as well as the problem of the motion of a single star in the principal plane of a galaxy. The methodical accuracy has been estimated by a comparison with the numerical solution. 相似文献
10.
Noboru Takeichi 《Celestial Mechanics and Dynamical Astronomy》2010,108(4):405-416
The parametric excitation of a gravity gradient stabilized spacecraft induced by the periodic solar pressure torque is discussed.
The solar pressure torque in the linearized equations of motion appears as linear terms with periodic coefficients. The attitude
stability is analyzed numerically through the calculation of the Floquet multiplier. The perturbation method is also applied
to identify the instability condition analytically. It is made clear that the periodic solar pressure torque can destabilize
the coupled roll and yaw attitude motion of the spacecraft. It is also shown that the conditions of parametric resonance are
included in the gravity gradient stability condition. Nonlinear simulations are also carried out to verify the effect of the
parametric resonance. The numerical simulation using actual parameters shows that the spacecraft inevitably experiences a
large amplitude attitude motion due to the periodic solar pressure torque even if the gravity gradient stability condition
is satisfied. 相似文献
11.
Fathi Namouni 《Monthly notices of the Royal Astronomical Society》2010,401(1):319-332
Dynamical friction arises from the interaction of a perturber and the gravitational wake it excites in the ambient medium. This interaction is usually derived assuming that the perturber has a constant velocity. In realistic situations, motion is accelerated as for instance by dynamical friction itself. Here, we study the effect of acceleration on the dynamical friction force. We characterize the density enhancement associated with a constantly accelerating perturber with rectilinear motion in an infinite homogeneous gaseous medium and show that dynamical friction is not a local force and that its amplitude may depend on the perturber's initial velocity. The force on an accelerating perturber is maximal between Mach 1 and Mach 2, where it is smaller than the corresponding uniform motion friction. In the limit where the perturber's size is much smaller than the distance needed to change the Mach number by unity through acceleration, a subsonic perturber feels a force similar to uniform motion friction only if its past history does not include supersonic episodes. Once an accelerating perturber reaches large supersonic speeds, accelerated motion friction is marginally stronger than uniform motion friction. The force on a decelerating supersonic perturber is weaker than uniform motion friction as the velocity decreases to a few times the sound speed. Dynamical friction on a decelerating subsonic perturber with an initial Mach number larger than 2 is much larger than uniform motion friction and tends to a finite value as the velocity vanishes in contrast to uniform motion friction. 相似文献
12.
David L. Richardson 《Celestial Mechanics and Dynamical Astronomy》1980,22(3):231-236
A lagrangian formulation for the three-dimensional motion of a satellite in the vicinity of the collinear points of the circular-restricted problem is reconsidered. It is shown that the influence of the primaries can be expressed in the form of two third-body disturbing functions. By use of this approach, the equations for the Lagrangian and for the motion itself are readily developed into highly compact expressions. All orders of the non-linear developments are shown to be easily obtainable using well-known recursive relationships. The resulting forms for these equations are well suited for use in the initial phase of canonical or non-canonical investigations. 相似文献
13.
The flow of a power law fluid past a symmetrical wedge is studied in the neighbourhood of the stagnation point when an external magnetic field is applied. The nonlinear equation of motion is transformed to a similarity differential equation which is solved using the method of successive approximations. The analytical solutions found by this method yield numerical values in good agreement with tabulated calculations obtained before via numerical methods for electrically nonconducting fluids. Analytical expressions are derived for both the velocity profile and the local non-dimensional skin friction coefficient. Also the three thicknesses of displacement, momentum and kinetic energy are given in closed forms. 相似文献
14.
The energy and the angular momentum integral of motion for the planar three point problem cannot assure bounded motion. In this paper it is shown that if one of the points is replaced by a homogeneous sphere then bounded motion can be found. The zero velocity surfaces for this modified problem are found and their evolution is described. 相似文献
15.
V. A. Shefer 《Solar System Research》2010,44(2):152-165
We propose a new method for the determination of the preliminary orbit of a small celestial body using three pairs of its
angular coordinates in three moments of time. The method is based on the use of the intermediate orbit we constructed earlier
using three position vectors and the corresponding time moments. This intermediate orbit accounts for the main part of the
perturbations of the motion of the body under study. We compare the results obtained by the classical Lagrange-Gauss method,
Herrick-Gibbs method, generalized Herrick-Gibbs method, and the new method by the examples of the determination of the orbit
of the small planet 1566 Icarus. The comparison showed that the new method is a highly efficient tool for the study of perturbed
motion. It is especially efficient when applied to high-precision observational data covering short arcs of the orbit. 相似文献
16.
N. D. Caranicolas 《Journal of Astrophysics and Astronomy》2001,22(4):309-319
We present a map for the study of resonant motion in a potential made up of two harmonic oscillators with quartic perturbing
terms. This potential can be considered to describe motion in the central parts of non-rotating elliptical galaxies. The map
is based on the averaged Hamiltonian. Adding on a semi-empirical basis suitable terms in the unperturbed averaged Hamiltonian,
corresponding to the 1:1 resonant case, we are able to construct a map describing motion in several resonant cases. The map
is used in order to find thex − p
x
Poincare phase plane for each resonance. Comparing the results of the map, with those obtained by numerical integration of
the equation of motion, we observe, that the map describes satisfactorily the broad features of orbits in all studied cases
for regular motion. There are cases where the map describes satisfactorily the properties of the chaotic orbits as well. 相似文献
17.
S. N. Kirpichnikov E. S. Kirpichnikova E. N. Polyakhova A. S. Shmyrov 《Celestial Mechanics and Dynamical Astronomy》1995,63(3-4):255-269
A complete treatment of the general motion of rotation and translation of a solar-sail spacecraft is proposed for the non-flat sail of complex shape. The planar heliocentric roto-translatory motion is considered, orbit-rotational coupling in the problem of altitude and orbital sail motion is investigated for the two-folding sail formed by two unequal reflective rectangular plates oriented at a right angle. The problem of orbit-rotational coupling is essentially a planar one: both sail plates are orthogonal to the orbital plane. The possibility of the non-controlled interplanetary transfer with such two-folding sail at its passive radiational orientation is established analytically from point of view of orbit-rotational coupling. Optimal geometric proportions of this sail are found at minimum-time interplanetary transfers. 相似文献
18.
Demetrios Gn. Fakis Tilemahos J. Kalvouridis 《Celestial Mechanics and Dynamical Astronomy》2013,116(3):229-240
This study outlines some aspects of the dynamics of a small body under the action of a Maxwell-type N-body system with a spheroidal central body. The non-sphericity of the central primary is described by means of a corrective term in the Newton’s law of gravitation and is taken into account during the derivation of the equations of motion of the small body, improving in this way, previous treatments. Based on this new consideration we investigate the equilibrium locations of the small body and their parametric dependence, as well as the zero-velocity curves and surfaces for the planar motion, and the evolution of the regions where this motion is permitted when the Jacobian constant varies. 相似文献
19.
E. E. Zotos 《Astronomische Nachrichten》2014,335(8):886-899
A three‐dimensional dynamical model for a galaxy hosting a BL Lacertae object is constructed. The model consists of a logarithmic potential representing an elliptical host galaxy with a bulge of radius cb and a dense massive nucleus. Using numerical experiments, we try to distinguish between regular and chaotic motion in both 2D and 3D system. In particular, we investigate how the basic parameters of our model, such as the mass of the nucleus, the internal perturbation and the flattening parameters influence the amount and the degree of chaos. Interesting correlations are presented for both 2D and 3D dynamical models. Our numerical results are explained and supported using elementary theoretical arguments and analytical calculations. Of particular interest is the local integral of motion which have been found to exist in the vicinity of stable periodic points. The obtained numerical outcomes of the present research are linked and also compared with several data derived from observations. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
20.
D. V. Mikryukov 《Astronomy Letters》2018,44(5):337-350
A system of averaged equations of planetary motion around a central star is constructed. An astrocentric coordinate system is used. The two-planet problem is considered, but all constructions are easily generalized to an arbitrary number N of planets. The motion is investigated in modified (complex) Poincarécanonical elements. The averaging is performed by the Hori–Deprit method over the fast mean longitudes to the second order relative to the planetary masses. An expansion of the disturbing function is constructed using the Laplace coefficients. Some terms of the expansion of the disturbing function and the first terms of the expansion of the averaged Hamiltonian are given. The results of this paper can be used to investigate the evolution of orbits with moderate eccentricities and inclinations in various planetary systems. 相似文献