共查询到20条相似文献，搜索用时 62 毫秒
1.
Carol Williams 《Celestial Mechanics and Dynamical Astronomy》1987,43(1-4):35-35
An attempt is made to find a representation of planetary perturbations which does not require a Fourier expansion. For the planetary type three body problem a sequence of canonical transformations is given based on Landen transformations coupled with a rescaling of the time. The expansion is carried out to the order 2 in the Hamiltonian. 相似文献
2.
Joachim Heimberger Michael Soffel Hanns Ruder 《Celestial Mechanics and Dynamical Astronomy》1989,47(2):205-217
The motion of artificial satellites in the gravitational field of an oblate body is discussed in the post — Newtonian framework using the technique of canonical Lie transformations. Two Lie transformations are used to derive explicit results for the longperiodic and secular perturbations for satellite orbits in the Einstein case. 相似文献
3.
Paul Nacozy 《Celestial Mechanics and Dynamical Astronomy》1976,13(4):495-501
A review and discussion of several investigations concerning the effect of time transformations on numerical integration errors is given. In particular, the discussion treats the relation between time transformations andlocal truncation errors. Additional numerical results are presented which indicate that time transformations reducelocal truncation errors. The results complement those of other studies, especially the recent studies of Danby, Wong, Velez, and Feagin and Mikkilineni. A Sundman time transformation with avarying exponent is introduced and discussed. 相似文献
4.
Paul E. Nacozy 《Celestial Mechanics and Dynamical Astronomy》1981,23(2):173-198
Time elements are introduced in terms of Keplerian (classical) orbital elements for use with time transformations of the Sundman type. Three different time elements are introduced. One time element is associated with the eccentric anomaly, a second time element is associated with the true anomaly, and a third time element is associated with theintermediate anomaly.Numerical results are presented that show accuracy improvements of from one to two orders of magnitude when time elements are employed along with Sundman time transformations, compared with using time transformations alone. 相似文献
5.
Michel Rapaport 《Celestial Mechanics and Dynamical Astronomy》1980,21(2):177-182
We use classical definitions and results of differential geometry in studying properties of transformations depending on a small parameter, acting on differential systems.Notions of one-parameter Lie's group of transformations, of bracket of vector fields (Lie's derivative) ard used. In the same way, the notion of symplectic manifold and of transformations which keep invariant a 2-form are useful.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978. 相似文献
6.
We derive the transformations to convert the state vector in cartesian coordinates into geometric orbital elements (and conversely
the geometric elements into the state vector) for a test particle moving around an oblate planet. These transformations arise
from the epicyclic theory and are accurate to second order in eccentricity and inclination. This paper is written to be directly
used for computational purposes, such as the numerical study of ring dynamics. 相似文献
7.
Ryan E. Sherrill Andrew J. Sinclair S. C. Sinha T. Alan Lovell 《Celestial Mechanics and Dynamical Astronomy》2014,119(1):55-73
The relative motion of chief and deputy satellites in close proximity with orbits of arbitrary eccentricity can be approximated by linearized time-periodic equations of motion. The linear time-invariant Hill–Clohessy–Wiltshire equations are typically derived from these equations by assuming the chief satellite is in a circular orbit. Two Lyapunov–Floquet transformations and an integral-preserving transformation are here presented which relate the linearized time-varying equations of relative motion to the Hill–Clohessy–Wiltshire equations in a one-to-one manner through time-varying coordinate transformations. These transformations allow the Hill–Clohessy–Wiltshire equations to describe the linearized relative motion for elliptic chief satellites. 相似文献
8.
J. Bryant 《Celestial Mechanics and Dynamical Astronomy》1981,25(1):41-49
The 1-parameter transformation groups (otherwise known as infinitesimal transformations) admitted by a system of differential equations are fundamental to the study of its properties. In this paper we first of all consider 1-parameter groups of contact transformations. Then, by generalizing Noether's theorem, we show how they are fundamental to what I call the Extended Hamiltonian System. Finally, this is illustrated by the extendedN-Body problem.
Resume Les groupes de transformations à 1 paramètre (appelés aussi transformations infinitésimales) admis par un systeme d'équations différentielles sont fondamentaux dans l'étude de ses propriétés. Dans cet article, nous considérons d'abord les groupes à 1 paramètre de transformations de contact. Ensuite, par la généralisation du théorème de Noether, nous montrons qu'ils sont fondamentaux dans l'étude de ce que j'appelle le Système Hamiltonien Etendu. Enfin ceci est illustré par le problème étendu desN-Corps.相似文献
9.
Theory of the motion of an artificial Earth satellite 总被引：1，自引：0，他引：1
Felix R. Hoots 《Celestial Mechanics and Dynamical Astronomy》1981,23(4):307-363
An improved analytical solution is obtained for the motion of an artificial Earth satellite under the combined influences of gravity and atmospheric drag. The gravitational model includes zonal harmonics throughJ
4, and the atmospheric model assumes a nonrotating spherical power density function. The differential equations are developed through second order under the assumption that the second zonal harmonic and the drag coefficient are both first-order terms, while the remaining zonal harmonics are of second order.Canonical transformations and the method of averaging are used to obtain transformations of variables which significantly simplify the transformed differential equations. A solution for these transformed equations is found; and this solution, in conjunction with the transformations cited above, gives equations for computing the six osculating orbital elements which describe the orbital motion of the satellite. The solution is valid for all eccentricities greater than 0 and less than 0.1 and all inclinations not near 0o or the critical inclination. Approximately ninety percent of the satellites currently in orbit satisfy all these restrictions. 相似文献
10.
C. E. Velez 《Celestial Mechanics and Dynamical Astronomy》1974,10(4):405-422
This paper deals with the implications of stability as applied to the numerical calculation of orbits. The study was motivated by the recent appearance of several proposed transformations of the classical Newtonian equations of motion which analytically stabilize Cowell's method. This report analyzes the basic properties of such stabilizing transformations and shows the removal of the period as a parameter is the key to these transformations and, that although such transformations do not yield global numerical error bounds, the error propagation properties are more favorable-linear vs quadratic growth.This paper was presented at the AIAA/AAS Astrodynamics Conference Vail, Colorado/July 16–18, 1973. 相似文献
11.
One of the main difficulties encountered in the numerical integration of the gravitationaln-body problem is associated with close approaches. The singularities of the differential equations of motion result in losses of accuracy and in considerable increase in computer time when any of the distances between the participating bodies decreases below a certain value. This value is larger than the distance when tidal effects become important, consequently,numerical problems are encounteredbefore the physical picture is changed. Elimination of these singularities by transformations is known as the process of regularization. This paper discusses such transformations and describes in considerable detail the numerical approaches to more accurate and faster integration. The basic ideas of smoothing and regularization are explained and applications are given. 相似文献
12.
C. Sivaram 《Astrophysics and Space Science》1993,207(2):317-324
The notion of discrete scale transformations is invoked to suggest strong links between fundamental interactions and cosmology giving rise to a hierarchy of cosmic scales. 相似文献
13.
The number of reference points for the fixing of a selenodetic reference frame in the Moon’s body is estimated. It is shown
that, for this purpose, from 40 to 100 reference points are sufficient. Precision of the selenodetic coordinate transformations
from one system to another is also analysed. 相似文献
14.
An analytical solution for the joint effects of the Earth oblateness and the direct solar radiation pressure on the motion
of an Artificial Earth Satellite of complex shape is constructed. The equations of motion are derived in the previous paper
(hereafter refered to as paper I). The solution is effected through two canonical transformations retaining secular and periodic
terms up to orders 3 and 2 respectively. The developments stressed on the effects of the radiation pressure and its coupling
with the earth's gravity. A procedure for the computation of position and velocity is outlined. The conditions of the resonance
are determined and the procedure for the transformations in the case of resonance is outlined. The solution revealed as expected
that radiation pressure produced secular effects at the third order resulting from the coupling between periodic terms at
lower orders. These affect both the main satellite body and the antenna.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
15.
We consider Sundman and Poincaré transformations for the long-time numerical integration of Hamiltonian systems whose evolution occurs at different time scales. The transformed systems are numerically integrated using explicit symplectic methods. The schemes we consider are explicit symplectic methods with adaptive time steps and they generalise other methods from the literature, while exhibiting a high performance. The Sundman transformation can also be used on non-Hamiltonian systems while the Poincaré transformation can be used, in some cases, with more efficient symplectic integrators. The performance of both transformations with different symplectic methods is analysed on several numerical examples. 相似文献
16.
Hawking’s radiation effect of Klein-Gordon equation, Dirac particles and Maxwell’s electromagnetic fields in the non-stationary rotating de Sitter cosmological space-time is investigated by using a new method of generalized tortoise coordinate transformation. It is found that the new transformation produces constant additional terms in the expressions of the surface gravities and the Hawking’s temperatures. If the constant terms are set to zero, then the surface gravities and Hawking’s temperatures will be equal to those obtained from the old generalized tortoise coordinate transformations. This shows that the new transformations are more reasonable. The Fermionic spectrum of Dirac particles displays a new spin-rotation coupling effect. 相似文献
17.
S. Bilir S. Ak S. Karaali A. Cabrera-Lavers T. S. Chonis C. M. Gaskell † 《Monthly notices of the Royal Astronomical Society》2008,384(3):1178-1188
We present colour transformations for the conversion of the Two Micron All Sky Survey (2MASS) photometric system to the Johnson–Cousins UBVRI system and further into the Sloan Digital Sky Survey (SDSS) ugriz system. We have taken SDSS gri magnitudes of stars measured with the 2.5-m telescope from SDSS Data Release 5 (DR5), and BVRI and JHK s magnitudes from Stetson's catalogue and Cutri et al., respectively. We matched thousands of stars in the three photometric systems by their coordinates and obtained a homogeneous sample of 825 stars by the following constraints, which are not used in previous transformations: (1) the data are dereddened, (2) giants are omitted and (3) the sample stars selected are of the highest quality. We give metallicity, population type and transformations dependent on two colours. The transformations provide absolute magnitude and distance determinations which can be used in space density evaluations at short distances where some or all of the SDSS ugriz magnitudes are saturated. The combination of these densities with those evaluated at larger distances using SDSS ugriz photometry will supply accurate Galactic model parameters, particularly the local space densities for each population. 相似文献
18.
José F. Cariñena Luis A. Ibort Ernesto A. Lacomba 《Celestial Mechanics and Dynamical Astronomy》1987,42(1-4):201-213
We show that time scaling transformations for Hamiltonian systems are infinitesimal canonical transformations in a suitable extended phase space constructed from geometrical considerations. We compute its infinitesimal generating function in some examples: regularization and blow up in celestial mechanics, classical mechanical systems with homogeneous potentials and Scheifele theory of satellite motion.Research partially supported by CONACYT (México), Grant PCCBBNA 022553 and CICYT (Spain). 相似文献
19.
Michel Rapaport 《Celestial Mechanics and Dynamical Astronomy》1976,13(2):217-227
We use classical definitions and results of differential geometry in studying properties of transformations depending on a small parameter, acting on differential systems. Hori's and Deprit's algorithms can be defined for these systems. A lemma is given to show these algorithms are equivalent. The so-called property of covariance is merely established. The canonical systems are then considered as associated with Hamiltonian vectorfields on symplectic manifolds. The property that the infinitesimal generator of a canonical transformation is an Hamiltonian vectorfield permits to establish separately the generality of Hori's and Deprit's algorithms. We suggest that the Hamiltonian vectorfield property can be extended to the generators of transformations depending on several parameters. 相似文献
20.
Transformations are given which change the perturbed planar problem of two bodies into unperturbed and undamped harmonic oscillators with constant coefficients. The orginally singular, nonlinear and Lyapunov unstable equations become in this way regular, linear, and the stable solution may be written down immediately in terms of the new variables. Transformations of the independent and dependent variables are treated separately as well as jointly. Using arbitrary and special functions for the transformations allows a systematic discussion of previously introduced and new anomalies. For the unperturbed two-body problem the theorem is proved according to which if the transformations are power-functions of the radial variable, then only the eccentric and the true anomalies with the corresponding transformations of the radial variable will result in harmonic oscillators. Important practical applications are to increase autonomous operations in space, since by replacing lengthy numerical integrations by transformations, computer requirements are significantly reduced. 相似文献