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1.
By Hamiltonian manipulation we demonstrate the existence of separable time‐transformed Hamiltonians in the extended phase‐space.
Due to separability explicit symplectic methods are available for the solution of the equations of motion. If the simple leapfrog
integrator is used, in case of two‐body motion, the method produces an exact Keplerian ellipse in which only the time‐coordinate
has an error. Numerical tests show that even the rectilinear N‐body problem is feasible using only the leapfrog integrator.
In practical terms the method cannot compete with regularized codes, but may provide new directions for studies of symplectic
N‐body integration.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
2.
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
3.
We define combinations of dual‐ and single‐satellite crossover differences to isolate both stationary orbit‐geopotential and
non‐geopotential errors in altimetry data. Specifically two types of combinations are found useful. While no combination of
differences can resolve the full radial error of single or paired satellites, an approximation of the mean or geographically
correlated error of the generally dominant lower orbit of a pair can be found from one kind (substitutions). (The variable
part of the error is always available from the single‐satellite crossover differences.) A second useful combination type is
found to yield no geopotential orbit error (zeros): uniquely, these can reveal errors in altimetry from imperfect media corrections
as well as oceanographic changes in sealevel. The later circumstance is particularly important when the missions for a pair
of satellites are disparate in time.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
4.
James E. Howard 《Celestial Mechanics and Dynamical Astronomy》1999,74(1):19-57
Relative equilibria occur in a wide variety of physical applications, including celestial mechanics, particle accelerators,
plasma physics, and atomic physics. We derive sufficient conditions for Lyapunov stability of circular orbits in arbitrary
axisymmetric gravitational (electrostatic) and magnetic fields, including the effects of local mass (charge) and current density.
Particularly simple stability conditions are derived for source‐free regions, where the gravitational field is harmonic (∇2U = 0) or the magnetic field irrotational (∇ × B = 0). In either case the resulting stability conditions can be expressed
geometrically (coordinate‐free) in terms of dimensionless stability indices. Stability bounds are calculated for several examples,
including the problem of two fixed centers, the J2 planetary model, galactic disks, and a toroidal quadrupole magnetic field.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
5.
In the free‐fall three‐body problem, distributions of escape, binary, and triple collision orbits are obtained. Interpretation
of the results leads us to the existence of oscillatory orbits in the planar three‐body problem with equal masses. A scenario
to prove their existence is described.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
6.
Juan Getino Pablo MartÍn JosÉ M. Farto 《Celestial Mechanics and Dynamical Astronomy》1999,74(3):153-162
In this paper, the previous nutation series corresponding to the rotation of a non‐rigid earth composed of a rigid mantle
and a liquid core obtained by Getino and Ferrándiz in 1997 are notably improved by using a high performance data fitting method.
This method can be applied to many other problems presenting a non‐linear dependence on the free parameters.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
7.
F. Varadi 《Celestial Mechanics and Dynamical Astronomy》1998,70(4):271-278
Perturbation theory of tori involves solving a first order partial differential equation, the so‐called homological equation.
The usual complete Fourier expansions employed in its solution can be replaced by partial ones. The alternative solution so
obtained is expressed in terms of integrals and without any explicit reference to trigonometric functions. Application to
second order averaging is also discussed.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
8.
G. A. krasinsky 《Celestial Mechanics and Dynamical Astronomy》1999,75(1):39-66
Analytical expressions for tidal torques induced by a tide‐arising planet which perturbs rotation of a nonrigid body are derived.
Corresponding expressions both for secular and periodic perturbations of the Euler's angles are given for the case of the
earth's rotation. Centennial secular rates of the nutation angle θ and of the earth's angular velocity ω, as well as the centennial
logarithmic decrement ν of the Chandler wobble are evaluated:
mas,
.
In the Universal Time (UT) a large out‐of‐phase (sine) dissipative term with the period 18.6 years and the amplitude 2.3 ms
is found. Corrections to nutation coefficients, which presumably have not been taken into account in IAU theory, are given.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
Irina Tupikova Michael Soffel Sergei Klioner 《Celestial Mechanics and Dynamical Astronomy》1999,74(3):147-152
Starting from the classical expansion of the perturbing function in the three‐body problem, the transformation to individual
orbital elements is performed in principle up to any degree in small parameters. Some corrections to the results presented
in the well‐known article by Yuasa on secular perturbations of asteroids are given. Consequences for the expansion of the
indirect part of the perturbing function are discussed.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
10.
V. Batllo 《Celestial Mechanics and Dynamical Astronomy》1998,71(3):191-201
The objective of this paper is to develop a simple model of an encounter between a comet and a planet, with a subsequent capture
or an escape, and to study the potential consequences. The hypothetical scenario is as follows: a comet with a conic orbit
meets close to one of its vertices (located near the ecliptic plane), a jovian planet, and transforms its orbit. There are
two hypotheses which are made for the shock: this vertex becomes one of the final vertices and the orbital plane of the comet
is unchanged during the encounter as it was the case for Brooks 2 in 1886.
In this model, it was able to find an equation which was then used to obtain the pre‐ and post‐encounter orbits elements and
the kind of orbit (ellipse, hyperbola, parabola) with respect to the initial inclination. The numerical experiments with the
observed comets often provide pre‐encounter orbits with an aphelion point located near another jovian planet farther from
the Sun, and so on with sometimes several planets, or with an aphelion point located beyond the Pluto orbit.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
11.
L. Benet T. H. Seligman D. Trautmann 《Celestial Mechanics and Dynamical Astronomy》1998,71(3):167-189
We study the scattering motion of the planar restricted three‐body problem for small mass parameters μ. We consider the symmetric
periodic orbits of this system with μ = 0 that collide with the singularity together with the circular and parabolic solutions
of the Kepler problem. These divide the parameter space in a natural way and characterize the main features of the scattering
problem for small non‐vanishing μ. Indeed, continuation of these orbits yields the primitive periodic orbits of the system
for small μ. For different regions of the parameter space, we present scattering functions and discuss the structure of the
chaotic saddle. We show that for μ < μc and any Jacobi integral there exist departures from hyperbolicity due to regions of
stable motion in phase space. Numerical bounds for μc are given.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
12.
F. Roosbeek 《Celestial Mechanics and Dynamical Astronomy》1999,74(4):243-252
In this paper, the series RDAN97 recently published (Roosbeek and Dehant, 1998) is completed by computing the diurnal and
subdiurnal nutation terms. The method used is based on computing the torque induced by the external bodies on the rigid earth.
The ephemerides used are analytical and based on celestial mechanics considerations. With a truncation level of 0.1 μas, 115
terms in longitude and 78 terms in obliquity have been computed. These terms correspond to the influence of the earth's geopotential
coefficients c2,2 and s2,2, c3,m and s3,m (for the interaction between the earth and the moon and the sun), and c4,m and s4,m (for the interaction between the earth and the moon). A comparison with the recent theories REN‐2000 (Souchay and Kinoshita,
1996, 1997) and SMART97 (Bretagnon et al., 1997, 1998) shows that our series is at a very high precision, better than the
most recent VLBI campaigns.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
13.
Seppo Mikkola 《Celestial Mechanics and Dynamical Astronomy》1999,74(4):275-285
The use of the extended phase space and time transformations for constructing efficient symplectic methods for computing the
long term behavior of perturbed two‐body systems are discussed. Main applications are for artificial satellite orbits. The
methods suggested here are efficient also for large eccentricities.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
14.
Bernard J. T. Jones 《Monthly notices of the Royal Astronomical Society》1999,307(2):376-386
I present an analytic model for non‐linear clustering of the luminous (baryonic) material in a universe in which the gravitational field is dominated by dark matter. The model is based on a two-component generalization of the adhesion approximation in which the gravitational potential of the dark component is determined by the standard Zel'dovich approximation or one of its variants, or by an N ‐body simulation. The baryonic matter flow is dissipative and is driven by this dark matter gravitational potential. The velocity potential of the matter is described by a generalization of the Burgers equation: the random heat equation ('RH equation') with a spatially correlated Gaussian driving potential.
The properties of the RH equation are well understood: it is closely related to the equation for the Anderson model and to Brownian motion in a random potential: the solution can be expressed in terms of path integrals. Using this it is possible to derive the scaling properties of the solution and, in particular, those of the resultant velocity field. Even though the flow is non‐linear, the velocity field remains Gaussian and inherits its scaling properties from the gravitational potential. This provides an underlying dynamical reason why the density field in the baryonic component is lognormally distributed and manifests multifractal scaling.
By explicitly putting dark and luminous matter on different footings, the model provides an improved framework for considering the growth of large‐scale cosmic structure. It provides a solution for the velocity potential of the baryonic component in closed form (albeit a path integral) from which the statistical properties of the baryonic flow can be derived. 相似文献
The properties of the RH equation are well understood: it is closely related to the equation for the Anderson model and to Brownian motion in a random potential: the solution can be expressed in terms of path integrals. Using this it is possible to derive the scaling properties of the solution and, in particular, those of the resultant velocity field. Even though the flow is non‐linear, the velocity field remains Gaussian and inherits its scaling properties from the gravitational potential. This provides an underlying dynamical reason why the density field in the baryonic component is lognormally distributed and manifests multifractal scaling.
By explicitly putting dark and luminous matter on different footings, the model provides an improved framework for considering the growth of large‐scale cosmic structure. It provides a solution for the velocity potential of the baryonic component in closed form (albeit a path integral) from which the statistical properties of the baryonic flow can be derived. 相似文献
15.
M. A. Sharaf Abdel-Naby S. Saad Amr A. Sharaf 《Celestial Mechanics and Dynamical Astronomy》1998,70(3):201-214
In this paper, a unified algorithm of Gauss method for near‐parabolic orbits that is valid for both elliptic and hyperbolic
cases is established symbolically and numerically.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
16.
marta Folgueira Jean Souchay Hiroshi Kinoshita 《Celestial Mechanics and Dynamical Astronomy》1998,70(3):147-157
In this paper, we make a study about the influence of the coefficients of the geopotential C4,m and S4,m, (m=1,2,3,4) on the nutation, starting from the Hamiltonian theory as developed by Kinoshita (1977).We obtain ten coefficients
larger than 0.05 μ as for the nutation in longitude and six for the nutation in obliquity. The present results are included
in the reconstruction of the theory of nutation (REN‐2000) at the level of truncation of 0.1 μ as (Souchay et al., 1997).
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
17.
The computation of the Earth's potential function at high order and degree with the method of reference [1], causes overflow
most of the time. The normalized method [2–6] can eliminate the overflows, but leads to formulae much more involved than those
in reference [1]; besides, the programming is more complex and the computer time required larger.
The method presented in this paper has the following features: each component of the satellite gravitational gradient can
be computed; the formulae are short and easy to be programme; the method is much quicker than the normalization method and
can be carried out with a micro‐computer, without overflow even in the case of Earth's spherical harmonics of order and degree
as high as 1025 or higher. This method satisfies the present demand to compute satellite gravitational gradient with high
accuracy.
Furthermore, we present formulae for the fast computation, without overflow, of the gravitational gradient corresponding to
Earth's spherical harmonics up to order and degree of 3170 × 3170 or higher.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
18.
We use the grid of hydrodynamic accretion disc calculations of Stehle to construct orbital phase‐dependent emission‐line profiles of thin discs carrying spiral density waves. The observational signatures of spiral waves are explored to establish the feasibility of detecting spiral waves in cataclysmic variable discs using prominent emission lines in the visible range of the spectrum. For high Mach number accretion discs ( M v φ c s ≃ 15 – 30), we find that the spiral shock arms are so tightly wound that they leave few obvious fingerprints in the emission lines. Only a minor variation of the double peak separation in the line profile at a level of ∼8 per cent is produced. For accretion discs in outburst ( M ≃ 5 – 20) however, the lines are dominated by the emission from an m =2 spiral pattern in the disc. We show that reliable Doppler tomograms of spiral shock patterns can be reconstructed provided that a signal‐to‐noise ratio of at least 15, a wavelength resolution of ∼80 km s−1 and a time resolution of ∼50 spectra per binary orbit are achieved. We confirm that the observed spiral pattern in the disc of IP Pegasi can be reproduced by tidal density waves in the accretion disc and demands the presence of a large, hot disc, at least in the early outburst stages. 相似文献
19.
The orbits of planetcrossing asteroids (and comets) can undergo close approaches and collisions with some major planet. This introduces a singularity in the Nbody Hamiltonian, and the averaging of the equations of motion, traditionally used to compute secular perturbations, is undefined. We show that it is possible to define in a rigorous way some generalised averaged equations of motion, in such a way that the generalised solutions are unique and piecewise smooth. This is obtained, both in the planar and in the threedimensional case, by means of the method of extraction of the singularities by Kantorovich. The modified distance used to approximate the singularity is the one used by Wetherill in his method to compute probability of collision. Some examples of averaged dynamics have been computed; a systematic exploration of the averaged phase space to locate the secular resonances should be the next step.'Alice sighed wearily. I think you might do something better with the time she said, than waste it asking riddles with no answers(Alice in Wonderland, L. Carroll) 相似文献
20.
E. Piña 《Celestial Mechanics and Dynamical Astronomy》1999,74(3):163-174
The motion of three particles, interacting by gravitational forces, is studied in a new coordinate system given by the principal
axes of inertia, as determined by Euler angles, and using the inertia principal moments and an auxiliar angle as coordinates.
The solution to the particular Lagrange case of the three‐body problem is reviewed and solved in these new coordinates.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献