共查询到20条相似文献，搜索用时 31 毫秒
1.
Celestial coordinate reference systems in curved space-time 总被引：1，自引：1，他引：0
S. M. Kopejkin 《Celestial Mechanics and Dynamical Astronomy》1988,44(1-2):87-115
2.
David Moss 《Astrophysics and Space Science》1983,97(1):213-216
For the case ofn planets, we derive Lagrange's secular planetary equations in terms of the Poincaré canonical variables, using the Jacobi-Radau set of origins, and referring to a common fixed plane. 相似文献
3.
William W. Hooker 《Celestial Mechanics and Dynamical Astronomy》1975,11(3):337-359
Equations of motion are derived for systems of rotationally interconnected bodies in which the terminal bodies may be flexible and the remaining bodies are rigid. The bodies may have an arbitrary topological tree arrangement; that is, there are no closed loops of bodies. This derivation extends earlier results for systems of interconnected rigid bodies only, and is much simpler than several other recent works on terminal flexible bodies. The model for a flexible body assumes that the elastic deformation is representable as a time-varying linear combination of given mode shapes.The paper also derives the appropriate form for gravitational terms, so that the equations can be used for flexible satellites. Also included are expressions for kinetic energy and angular momentum so that in case these are theoretically constant, they can be used to monitor the accuracy of the numerical integration. The paper concludes with a section showing how interbody constraint forces and torques (which do not appear in the equations of motion) can be recovered from quantities available in this formulation, and also how to treat state variables which are prescribed functions of time.A digital computer program based on the equations derived here has been used to simulate a spinning Skylab (with flexible booms) and also the interplanetary Viking (with flexible solar panels and thrust vector control).We announce with regret that Bill Hooker died in an avalanche while on a mountain-climbing expedition in Peru, July 1974. 相似文献
4.
David Parry Rubincam 《Celestial Mechanics and Dynamical Astronomy》1977,15(1):21-33
The motion of a satellite with negligible mass in the Schwarzschild metric is treated as a problem in Newtonian physics. The relativistic equations of motion are formally identical with those of the Newtonian case of a particle moving in the ordinary inverse-square law field acted upon by a disturbing function which varies asr ?3. Accordingly, the relativistic motion is treated with the methods of celestial mechanics. The disturbing function is expressed in terms of the Keplerian elements of the orbit and substituted into Lagrange's planetary equations. Integration of the equations shows that a typical Earth satellite with small orbital eccentricity is displaced by about 17 cm from its unperturbed position after a single orbit, while the periodic displacement over the orbit reaches a maximum of about 3 cm. Application of the equations to the planet Mercury gives the advance of the perihelion and a total displacement of about 85 km after one orbit, with a maximum periodic displacement of about 13 km. 相似文献
5.
André Deprit 《Celestial Mechanics and Dynamical Astronomy》1983,30(2):181-195
In application of the Reduction Theorem to the general problem ofn (>-3) bodies, a Mathieu canonical transformation is proposed whereby the new variables separate naturally into (i) a coordinate system on any reduced manifold of constant angular momentum, and (ii) a quadruple made of a pair of ignorable longitudes together with their conjugate momenta. The reduction is built from a binary tree of kinetic frames Explicit transformation formulas are obtained by induction from the top of the tree down to its root at the invariable frame; they are based on the unit quaternions which represent the finite rotations mapping one vector base onto another in the chain of kinetic frames. The development scheme lends itself to automatic processing by computer in a functional language. 相似文献
6.
M. J. Miketinac 《Astrophysics and Space Science》1975,35(2):349-362
Polytropic models of axially-symmetric equilibrium stars of infinite conductivity with poloidal magnetic fields are constructed by numerical integration of the exact equations governing internal structure. The mathematical method used, a further generalization and improvement of Stoeckly's method, allows the construction of a sequence of equilibrium models starting with a spherically symmetric star (when no magnetic field is present) and terminating with a doughnut-shaped object (for a very strong magnetic field) — a fact already shown by Monaghan. Detailed results are given only for two polytropes with the indexn=1.5 and 3.0, although any other value ofn greater than or equal to one could have been selected. Contrary to Monaghan's results, it is found that along the sequence of configurations forn=3.0 the ratio of the magnetic and gravitational energy peaks out before a doughnut-shaped configuration is reached; but this effect does not characterize then=1.5 sequence. The calculations confirm, however, another result of Monaghan asserting that the magnetic field is a fairly insensitive function of the polytropic index. 相似文献
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9.
C. C. Leiby Jr. 《Astrophysics and Space Science》1972,17(2):368-377
The Maxwell equations for gravitational fields previously assumed by Sciama are derived from elementary considerations. The
Lagrangian for a gravitating mass in a non-inertial coordinate system yields equations of motion leading to force definitions
for a gravitational field intensity and a gravitational induction field. The non-inertial velocity of the coordinate system
plays the role of a vector potential contributing to the generalized momenta of bodies moving in the system. A Lagrangian
density constructed from the force-defined fields then lead to the source definitions of gravitational fields. It is found
that positive field energy densities require repulsive gravitational forces, whereas attractive forces imply the violation
of the conservation of energy. This paradox is resolved by representing gravitational quantities as pure-imaginary entities.
Thus characterized, the equations which define gravitational fields become identical to Maxwell's equations but are pure-imaginary.
This suggests a combined representation for gravitational and electromagnetic fields which, in covariant form, indicates both
the well known equivalence of mass and energy and a possible equivalence of charge and energy. From orthogonality considerations,
it is conjectured that this latter energy is gravitational, and that, whereas gravitational fields interact with electromagnetic
energy, electromagnetic fields interact with gravitational energy.
Parts of this work were completed at Air Force Cambridge Research Laboratories, Bedford, Mass., U.S.A. 相似文献
10.
Christoph Lhotka 《Celestial Mechanics and Dynamical Astronomy》2017,127(4):397-428
In this paper, we consider the elliptic collinear solutions of the classical n-body problem, where the n bodies always stay on a straight line, and each of them moves on its own elliptic orbit with the same eccentricity. Such a motion is called an elliptic Euler–Moulton collinear solution. Here we prove that the corresponding linearized Hamiltonian system at such an elliptic Euler–Moulton collinear solution of n-bodies splits into \((n-1)\) independent linear Hamiltonian systems, the first one is the linearized Hamiltonian system of the Kepler 2-body problem at Kepler elliptic orbit, and each of the other \((n-2)\) systems is the essential part of the linearized Hamiltonian system at an elliptic Euler collinear solution of a 3-body problem whose mass parameter is modified. Then the linear stability of such a solution in the n-body problem is reduced to those of the corresponding elliptic Euler collinear solutions of the 3-body problems, which for example then can be further understood using numerical results of Martínez et al. on 3-body Euler solutions in 2004–2006. As an example, we carry out the detailed derivation of the linear stability for an elliptic Euler–Moulton solution of the 4-body problem with two small masses in the middle. 相似文献
11.
George Bozis 《Celestial Mechanics and Dynamical Astronomy》1983,31(1):43-51
Any two of the componentsX, Y, andZ of an autonomous force field which gives rise to the space orbitsF(x, y, z)=c 1,G(x, y, z)=c 2 are related by a partial differential equation with coefficients depending on the functionsF andG. This is a generalization of the corresponding equation for planar orbits (Bozis, 1983). The above partial differential equation is accompanied by the algebraic linear equation inX, Y, andZ expressing the fact that the force vector is lying in the osculating plane at each point of the orbit. The two equations constitute a generalization of the corresponding Szebehely's equations in the three dimensional space (Érdi, 1982). The generalization is meant in the sense that the dynamical system is not necessarily assumed to be conservative. 相似文献
12.
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
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14.
W. Velte 《Celestial Mechanics and Dynamical Astronomy》1978,17(4):395-403
In this note we give by means of quaternions in vector notation a new derivation of the KS-transformation acting from a four-dimensional parameter space into the three-dimensional physical space. Using quaternions in vector notation each step in the derivation has an immediate geometrical interpretation. In particular, the KS-transformation appears as the Levi-Civita transformation, formulated in a rotated coordinate system.Dedicated to Professor Otto Volk. 相似文献
15.
Assuming that the orientation of a pulsar’s velocity vector is parallel to its spin axis, we have calculated the space velocities of 61 pulsars from their tangential velocities. The mean space velocity of the sample is equal to 267 km s-1. The radial velocities and kinematical ages of 20 pulsars are obtained. The decay time of the magnetic field of pulsars is τD = 2 Myr, smaller than previously found 相似文献
16.
A locally rotationally symmetric Bianchi type-II (LRS B-II) space-time with variable equation of state (EoS) parameter and
constant deceleration parameter have been investigated in the scalar-tensor theory proposed by Saez and Ballester (Phys. Lett.
A 113:467, 1986). The scalar-tensor field equations have been solved by applying variation law for generalized Hubble’s parameter given by
Bermann (Nuovo Cimento 74:182, 1983). The physical and kinematical properties of the model are also discussed. 相似文献
17.
Rotational dynamics of celestial bodies: Generalized rotation and considerations of angular momentum
V. S. Geroyannis 《Astrophysics and Space Science》1984,102(2):255-261
The transformation equations under generalized rotation are obtained for an initially defined reduced velocity tensor governing the motion of a deformable finite material continuum. Then angular momentum considerations lead to relations between flow properties of the continuum and properties of a coordinate system introduced to describe generalized rotation of the continuum. Such relations could define preferable coordinate systems perceiving zero angular momentum for the continuum or referring that it moves according to linear laws. 相似文献
18.
Vladimír Majerník 《Astrophysics and Space Science》1982,84(1):191-204
The Maxwell-like gravitational field equations have been generalized and coupled through the gravitational four-potential on the electromagnetic Maxwell's equations. It is shown that this has several astrophysical consequences, of which the main are the following (i) the gravitational instability of a system of mass bodies manifesting itself by a Hubble-like motion on cosmological scales, (ii) the possible change of light intensity propagating through a large distance (and so a possible change of the real energy output of some very distant objects, e.g., quasars), (iii) non-stability of a planetary system on the cosmological time scales, due to the momentum increase of the moving bodies in a generalized gravitational field. 相似文献
19.
In this paper we have deduced the differential equations of motion of the restricted problem of three bodies with decreasing mass, under the assumption that the mass of the satellite varies with respect to time. We have applied Jeans law and the space time transformation contrast to the transformation of Meshcherskii. The space time transformation is applicable only in the special casen=1,k=0,q=1/2. The equations of motion of our problem differ from the equations of motion of the restricted three body problem with constant mass only by small perturbing forces. 相似文献
20.
Nawsad Ali 《Journal of Astrophysics and Astronomy》2013,34(3):259-271
The present study deals with spatially homogeneous and anisotropic axially symmetric Bianchi type-I cosmological model with time variable cosmological term Λ in the presence of bulk viscous fluid. The Einstein’s field equations are solved explicitly by time varying deceleration parameter q. Consequences of the four cases of phenomenological decay of Λ have been discussed which are consistent with observations. Physical and kinematical parameters of the models are discussed. 相似文献