共查询到20条相似文献，搜索用时 156 毫秒
1.
Mohammed Adel Sharaf Mervat El-Sayed Awad Samiha Al-Sayed Abdullah Najmuldeen 《Earth, Moon, and Planets》1992,56(2):141-164
In this paper, the classical and generalized Sundman time transformations are used to establish new generating set of differential equations of motion in terms of the Eulerian redundant parameters. The implementation of this set on digital computers for the commonly used independent variables is developed once and for all. Motion prediction algorithms based on these equations are developed in a recursive manner for the motions in the Earth's gravitational field with axial symmetry whatever the number of the zonal harmonic terms may be. Applications for the two types of short and long term predictions are considered for the perturbed motion in the Earth's gravitational field with axial symmetry with zonal harmonic terms up to J
36
. Numerical results proved the very high efficiency and flexibility of the developed equations. 相似文献
2.
I. V. Tupikova 《Celestial Mechanics and Dynamical Astronomy》2009,104(1-2):129-144
A new mathematically correct approach to construct an averaging procedure for the motion of a massless body around the central body perturbed by fully interacting planets is developed and the errors of the standard solution are discussed. The new technique allows to combine the advantages of the Hamiltonian representation with the usage of standard osculating elements in combination with all the standard expansions of the perturbing functions. The main idea is to introduce new additional variables conjugate to all the standard elements and to work in a corresponding super phase space. In this way, the number of variables is doubled at first, but one has to deal with only one Hamiltonian. The artificially introduced variables disappear from the final averaged equations as well as from the transformation formulae connecting the osculating and the mean elements. 相似文献
3.
4.
J. M. Ferrándiz 《Celestial Mechanics and Dynamical Astronomy》1987,41(1-4):343-357
In this paper, we present a canonical transformation that extends the change of coordinates of Cartesian type into the associate homogeneous coordinates, and provides a redundant set of eight canonical variables to describe the orbital motion of a particle. The transformed problem has two additional integrals, since the transformation increases the number of variables. Using these variables and a time proportional to the true anomaly, the Kepler problem can be reduced to a 4-dimensional oscillator, whose frequency can be selected to be either the magnitude of the angular momentum or unity, depending on a suitable scaling.Perturbed problems are represented by perturbed harmonic oscillators, whatever the type of the orbit is, and in the special case of central force fields, the resulting equations can be linearized exactly. 相似文献
5.
Douglas C. Heggie 《Celestial Mechanics and Dynamical Astronomy》1974,10(2):217-241
The work of Aarseth and Zare (1974) is extended to provide aglobal regularisation of the classical gravitational three-body problem: by transformation of the variables in a way that does not depend on the particular configuration, we obtain equations of motion which are regular with respect to collisions between any pair of particles. The only cases excepted are those in which collisions between more than one pair occur simultaneously and those in which at least one of the masses vanishes. However, by means of the same principles the restricted problem is regularised globally if collisions between the two primaries are excluded. Results of numerical tests are summarised, and the theory is generalised to provide global regularisations, first, for perturbed three-body motion and, second, for theN-body problem. A way of increasing the number of degrees of freedom of a dynamical system is central to the method, and is the subject of an Appendix. 相似文献
6.
Brian L. Smith 《Astrophysics and Space Science》1977,47(1):61-78
It was shown in a previous paper (Smith, 1976) that the method of strained coordinates may be usefully employed in the determination of the structure of rotating polytropes. In the present work this idea is extended to Main-Sequence stars with conservative centrifugal fields. The structure variables, pressure, density and temperature are considered pure functions of an auxiliary coordinates (the strained coordinate) and the governing equations written in a form that closely resembles the structure equations for spherical stars but with correction factors that are functions ofs. A systematic, order-by-order derivation of these factors is outlined and applied in detail to a Cowling-model star in uniform rotation. The technique can be extended beyond first order and external boundary conditions are applied, as they should be, at the true surface of the star. Roche approximations are not needed. 相似文献
7.
R. Broucke 《Celestial Mechanics and Dynamical Astronomy》1978,18(3):207-222
In this article we study a form of equations of motion which is different from Lagrange's and Hamilton's equations: Pfaff's equations of motion. Pfaff's equations of motion were published in 1815 and are remarkably elegant as well as general, but still they are much less well known. Pfaff's equations can also be considered as the Euler-Lagrange equations derived from the linear Lagrangian rather than the usual Lagrangian which is quadratic in the velocity components. The article first treats the theory of changes of variables in Pfaff's equations and the connections with canonical equations as well as canonical transformations. Then the applications to the perturbed two-body problem are treated in detail. Finally, the Pfaffians are given in Hill variables and Scheifele variables. With these two sets of variables, the use of the true anomaly as independent variable is also considered. 相似文献
8.
The classical Poisson equations of rotational motion are used to study the attitude motions of an Earth orbiting, rapidly spinning gyroscope perturbed by the effects of general relativity (Einstein theory). The center of mass of the gyroscope is assumed to move about a rotating oblate Earth in an evolving elliptic orbit which includes all first-order oblateness effects produced by the Earth.A method of averaging is used to obtain a transformation of variables, for the nonresonance case, which significantly simplifies the Poisson differential equations of motion of the gyroscope. Longterm solutions are obtained by an exact analytical integration of the simplified transformed equations. These solutions may be used to predict both the orientation of the gyroscope and the motion of its rotational angular momentum vector as viewed from its center of mass. The results are valid for all eccentricities and all inclinations not near the critical inclination.This paper represents a part of the author's Ph. D. dissertation for the Mathematics Department, Auburn University. 相似文献
9.
The problem of finding natural bounded relative trajectories between the different units of a distributed space system is of great interest to the astrodynamics community. This is because most popular initialization methods still fail to establish long-term bounded relative motion when gravitational perturbations are involved. Recent numerical searches based on dynamical systems theory and ergodic maps have demonstrated that bounded relative trajectories not only exist but may extend up to hundreds of kilometers, i.e., well beyond the reach of currently available techniques. To remedy this, we introduce a novel approach that relies on neither linearized equations nor mean-to-osculating orbit element mappings. The proposed algorithm applies to rotationally symmetric bodies and is based on a numerical method for computing quasi-periodic invariant tori via stroboscopic maps, including extra constraints to fix the average of the nodal period and RAAN drift between two consecutive equatorial plane crossings of the quasi-periodic solutions. In this way, bounded relative trajectories of arbitrary size can be found with great accuracy as long as these are allowed by the natural dynamics and the physical constraints of the system (e.g., the surface of the gravitational attractor). This holds under any number of zonal harmonics perturbations and for arbitrary time intervals as demonstrated by numerical simulations about an Earth-like planet and the highly oblate primary of the binary asteroid (66391) 1999 KW4. 相似文献
10.
José Manuel Ferrándiz Ana Fernández-Ferreiros 《Celestial Mechanics and Dynamical Astronomy》1991,52(1):1-12
In this paper we consider the reduction of the equations of motion for non-planar perturbed two body problems into linear form. It is seen that this can be easily accomplished for any element of the class of radial intermediaries to the satellite problem proposed by Deprit in 1981, since they have a functional dependence suitable for linearization. The transformation is worked out by using an adequate set of redundant variables. Four harmonic oscillators are obtained, of which two are coupled through gyroscopic terms. Their constant frequencies contain the secular contribution of the main problem of artificial satellite theory up to the order of the considered intermediary. Therefore, this result may well be interesting in relation to the study and prediction of accurate long-term solutions to satellite problems. 相似文献
11.
We derive strong constraints on the Yukawa couplings and the vacuum expectation value in the singlet majoron model. The presence of a small gravitationally induced mass for the majoron can be used to set a constraint on its vacuum expectation value. If the singlet symmetry breaking scale is larger than the electroweak symmetry breaking scale, lepton number violating interactions in equilibrium with electroweak sphaleron interactions would destroy any prior baryon asymmetry. If the baryon asymmetry is not generated at the electroweak scale or later, strong bounds on the Yukawa couplings h 10−7 and VEVs vs < vEW are derived. We also carefully rederive baryogenesis bounds on neutrino masses, finding that in general they apply not to the masses themselves, but only to related parameters, and they are numerically somewhat less stringent than has previously been claimed. 相似文献
12.
Rafael Cubarsi 《Monthly notices of the Royal Astronomical Society》2007,380(2):848-864
The exact mathematical expression for an arbitrary n th-order stellar hydrodynamic equation is explicitly obtained depending on the central moments of the velocity distribution. In such a form the equations are physically meaningful, since they can be compared with the ordinary hydrodynamic equations of compressible, viscous fluids. The equations are deduced without any particular assumptions about symmetries, steadiness or particular kinematic behaviours, so that they can be used in their complete form, and for any order, in future works with improved observational data. Also, in order to work with a finite number of equations and unknowns, which would provide a dynamic model for the stellar system, the n th-order equation is needed to investigate in a more general way the closure conditions, which may be expressed in terms of velocity distribution statistics. A case example for a Schwarzschild distribution shows how the infinite hierarchy of hydrodynamic equations is reduced to the equations of orders n = 0, 1, 2, 3 , owing to the recurrent form of the central moments and to the equations of order n = 2 and 3, which become closure conditions for higher even- and odd-order equations, respectively. The closure example is generalized to a quadratic function in the peculiar velocities, so that the equivalence between moment equations and the system of equations that Chandrasekhar had obtained working from the collisionless Boltzmann equation is borne out. 相似文献
13.
S. G. Turyshev B-G. Andersson 《Monthly notices of the Royal Astronomical Society》2003,341(2):577-582
We have studied the science rationale, goals and requirements for a mission aimed at using the gravitational lensing from the Sun as a way of achieving high angular resolution and high signal amplification. We find that such a mission concept is compromised by several practical problems. Most severe are the effects due to the plasma in the solar atmosphere which cause refraction and scattering of the propagating rays. These effects either limit the frequencies that can be observed to those above ∼1 THz, or they move the optical point outwards beyond the vacuum value of ≥550 au. (Thus for observing frequency of 300 GHz the optical point is moved outwards to ∼ 680 au.) Density fluctuations in the inner solar atmosphere will further cause random pathlength differences for different rays. The corrections for the radiation from the Sun itself will also be a major challenge at any wavelength used, but could be mitigated with coronographic techniques. Given reasonable constraints on the spacecraft (particularly in terms of size and propulsion), source selection as well as severe navigational constraints further add to the difficulties for a potential mission. Nevertheless, unbiased surveys of small-scale structure on the sky at short wavelengths might be the most promising application of such a mission. 相似文献
14.
E. V. Polyachenko V. L. Polyachenko I. G. Shukhman 《Monthly notices of the Royal Astronomical Society》2007,379(2):573-596
We study spherical and disc clusters in a near-Keplerian potential of galactic centres or massive black holes. In such a potential orbit precession is commonly retrograde, that is, the direction of the orbit precession is opposite to the orbital motion. It is assumed that stellar systems consist of nearly-radial orbits. We show that if there is a loss-cone at low angular momentum (e.g. due to consumption of stars by a black hole), an instability similar to loss-cone instability in plasma may occur. The gravitational loss-cone instability is expected to enhance black hole feeding rates. For spherical systems, the instability is possible for the number of spherical harmonics l ≥ 3 . If there is some amount of counter-rotating stars in flattened systems, they generally exhibit the instability independent of azimuthal number m . The results are compared with those obtained recently by Tremaine for distribution functions monotonically increasing with angular momentum.
The analysis is based on simple characteristic equations describing small perturbations in a disc or a sphere of stellar orbits highly elongated in radius. These characteristic equations are derived from the linearized Vlasov equations (combining the collisionless Boltzmann kinetic equation and the Poisson equation), using the action-angle variables. We use two techniques for analysing the characteristic equations: the first one is based on preliminary finding of neutral modes, and the second one employs a counterpart of the plasma Penrose–Nyquist criterion for disc and spherical gravitational systems. 相似文献
The analysis is based on simple characteristic equations describing small perturbations in a disc or a sphere of stellar orbits highly elongated in radius. These characteristic equations are derived from the linearized Vlasov equations (combining the collisionless Boltzmann kinetic equation and the Poisson equation), using the action-angle variables. We use two techniques for analysing the characteristic equations: the first one is based on preliminary finding of neutral modes, and the second one employs a counterpart of the plasma Penrose–Nyquist criterion for disc and spherical gravitational systems. 相似文献
15.
Douglas C. Heggie 《Celestial Mechanics and Dynamical Astronomy》1976,14(1):69-71
It has been shown (Heggie, 1974) that the equations of motion for the three-body problem may be cast into a form which is regular for collisions betweenany pair of bodies. The method proceeds by two stages, namely
The present contribution gives a different treatment of the first of these stages, and relates the redundant variables to those introduced by Broucke and Lass (1973). 相似文献
| (i) | the introduction of redundant variables |
| (ii) | the application of the KS-transformation. |
16.
Angelo J. Skalafuris 《Astrophysics and Space Science》1969,3(2):234-257
We examine the problem of a shock wave propagating in a gravitational field in the presence of pressure and density gradients by attacking the non-linear equations of fluid flow. Our approach is analytical rather than numerical, and we analyze the characteristic equations of a fluid in the presence of gravity with radiative dissipation. Because the radiation field enters the fluid equations in the form of an integral, radiative dissipation may be considered an inhomogeneity which does not affect the characteristic directions. The fluid equations remain hyperbolic and thus are amenable to solution by the standard techniques of gas analysis.We give an equation of path for a shock wave and we enumerate the physical conditions which lead to stability or instability. We find that shock waves are generally unstable in most stellar atmospheres unless they are very weak. The form of the instability is that of a spicule deformation similar to that observed in the upper solar chromosphere.This work was carried out at the Smithsonian-Harvard Astrophysical Observatory and was presented in a thesis to Brandeis University, May 1963. 相似文献
17.
In the method of variation of parameters we express the Cartesian coordinates or the Euler angles as functions of the time
and six constants. If, under disturbance, we endow the “constants” with time dependence, the perturbed orbital or angular
velocity will consist of a partial time derivative and a convective term that includes time derivatives of the “constants”.
The Lagrange constraint, often imposed for convenience, nullifies the convective term and thereby guarantees that the functional
dependence of the velocity on the time and “constants” stays unaltered under disturbance. “Constants” satisfying this constraint
are called osculating elements. Otherwise, they are simply termed orbital or rotational elements. When the equations for the
elements are required to be canonical, it is normally the Delaunay variables that are chosen to be the orbital elements, and
it is the Andoyer variables that are typically chosen to play the role of rotational elements. (Since some of the Andoyer
elements are time-dependent even in the unperturbed setting, the role of “constants” is actually played by their initial values.)
The Delaunay and Andoyer sets of variables share a subtle peculiarity: under certain circumstances the standard equations
render the elements nonosculating. In the theory of orbits, the planetary equations yield nonosculating elements when perturbations
depend on velocities. To keep the elements osculating, the equations must be amended with extra terms that are not parts of the disturbing function [Efroimsky, M., Goldreich, P.: J. Math. Phys. 44, 5958–5977 (2003); Astron. Astrophys. 415, 1187–1199 (2004); Efroimsky, M.: Celest. Mech. Dyn. Astron. 91, 75–108 (2005); Ann. New York Acad. Sci. 1065, 346–374 (2006)]. It complicates both the Lagrange- and Delaunay-type planetary equations and makes the Delaunay equations
noncanonical. In attitude dynamics, whenever a perturbation depends upon the angular velocity (like a switch to a noninertial
frame), a mere amendment of the Hamiltonian makes the equations yield nonosculating Andoyer elements. To make them osculating,
extra terms should be added to the equations (but then the equations will no longer be canonical). Calculations in nonosculating
variables are mathematically valid, but their physical interpretation is not easy. Nonosculating orbital elements parameterise
instantaneous conics not tangent to the orbit. (A nonosculating i may differ much from the real inclination of the orbit, given by the osculating i.) Nonosculating Andoyer elements correctly describe perturbed attitude, but their interconnection with the angular velocity
is a nontrivial issue. The Kinoshita–Souchay theory tacitly employs nonosculating Andoyer elements. For this reason, even
though the elements are introduced in a precessing frame, they nevertheless return the inertial velocity, not the velocity
relative to the precessing frame. To amend the Kinoshita–Souchay theory, we derive the precessing-frame-related directional
angles of the angular velocity relative to the precessing frame. The loss of osculation should not necessarily be considered
a flaw of the Kinoshita–Souchay theory, because in some situations it is the inertial, not the relative, angular velocity
that is measurable [Schreiber, K. U. et al.: J. Geophys. Res. 109, B06405 (2004); Petrov, L.: Astron. Astrophys. 467, 359–369 (2007)]. Under these circumstances, the Kinoshita–Souchay formulae for the angular velocity should be employed (as
long as they are rightly identified as the formulae for the inertial angular velocity). 相似文献
18.
High‐resolution observations, made with the Very Large Array (VLA) at 330 MHz, 1.4 GHz and 8.4 GHz and with the Ryle Telescope at 15 GHz, are presented of a sample of 23 sources which are variable at 151 MHz, concluding the observations of an unbiased sample of 40 such sources. The 8.4 GHz emission of almost all of the sources is dominated by structure on a scale ≲0.1 arcsec – the spectra of these compact components are such that they will also dominate the emission at 151 MHz; the number of sources for which this is not the case is consistent with the number of spurious variables expected to be found in the sample. About two-thirds of the sources have the self-absorbed, or flat, spectra expected from their size. The majority (∼75 per cent) of the sources belong to the compact steep-spectrum (CSS) class, but are generally more compact than other CSS sources; the CSS variables also appear to exhibit more spectral ageing than typical CSS sources, which may indicate a difference in the nature of the sources. 相似文献
19.
S. Ferraz-Mello 《Celestial Mechanics and Dynamical Astronomy》1987,43(1-4):69-89
This review considers the problem of the construction of formal solutions for resonant systems and several concepts related to resonance. In the first part we introduce the concepts of Hori's kernel and averaging (not to be confounded with the usual Krylov-Bogolyubov first-order definition of averaging). In the second part these concepts are used to discuss resonance in action-angle variables. The first averaging, the construction of resonant Hori's kernels, their topological and quantitative constraints, the second averaging and the occurrence of inner resonances are discussed. These topics are assembled without a preoccupation of reviewing the contributions of all authors that have dealt with them, but rather aiming at giving a global picture of the problem of the construction of complete theories. 相似文献
20.
G. Bressanin 《Celestial Mechanics and Dynamical Astronomy》1970,2(1):77-87
The gaussian noise which affects tracking measurements causes an error in the computed value of the orbit parameters. This study provides a method for evaluating: (a) the length of the arc over which the satellite must be tracked; (b) the number of measurements to be made along this arc; (c) the position of the arc with respect to the orbit, necessary to reach the desired accurary of the calculated orbit parameters for a given pointing error of the tracking antenna. It has been assumed that the errors of the tracking measurements have a known gaussian probability distribution, which may differ for each measurement. The equations relating the orbit parameters to the measurements performed have been linearized. It has been shown that the orbit parameters are gaussian random variables and their variance has been calculated as a function of (a), (b) and (c).This paper was presented at the AIAA/AAS meeting, Princeton University, August 1969. 相似文献