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1.
The importance of the stability characteristics of the planar elliptic restricted three-body problem is that they offer insight
about the general dynamical mechanisms causing instability in celestial mechanics. To analyze these concerns, elliptic–elliptic
and hyperbolic–elliptic resonance orbits (periodic solutions with lower period) are numerically discovered by use of Newton's
differential correction method. We find indications of stability for the elliptic–elliptic resonance orbits because slightly
perturbed orbits define a corresponding two-dimensional invariant manifold on the Poincaré surface-section. For the resonance
orbit of the hyperbolic–elliptic type, we show numerically that its stable and unstable manifolds intersect transversally
in phase-space to induce instability. Then, we find indications that there are orbits which jump from one resonance zone to
the next before escaping to infinity. This phenomenon is related to the so-called Arnold diffusion.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
2.
Antonio Giorgilli Ugo Locatelli Marco Sansottera 《Celestial Mechanics and Dynamical Astronomy》2014,119(3-4):397-424
We give a constructive proof of the existence of elliptic lower dimensional tori in nearly integrable Hamiltonian systems. In particular we adapt the classical Kolmogorov normalization algorithm to the case of planetary systems, for which elliptic tori may be used as replacements of elliptic Keplerian orbits in Lagrange-Laplace theory. With this paper we support with rigorous convergence estimates the semi-analytic work in our previous article (Sansottera et al., Celest Mech Dyn Astron 111:337–361, 2011), where an explicit calculation of an invariant torus for a planar model of the Sun-Jupiter-Saturn-Uranus system has been made. With respect to previous works on the same subject we exploit the characteristic of Lie series giving a precise control of all terms generated by our algorithm. This allows us to slightly relax the non-resonance conditions on the frequencies. 相似文献
3.
Nonlinear dynamical analysis and the control problem for a displaced orbit above a planet are discussed. It is indicated that
there are two equilibria for the system, one hyperbolic (saddle) and one elliptic (center), except for the degenerate h
z
max, a saddle-node bifurcation point. Motions near the equilibria for the nonresonance case are investigated by means of the
Birkhoff normal form and dynamical system techniques. The Kolmogorov–Arnold–Moser (KAM) torus filled with quasiperiodic trajectories
is measured in the τ 1 and τ 2 directions, and a rough algorithm for calculating τ 1 and τ 2 is proposed. A general iterative algorithm to generate periodic Lyapunov orbits is also presented. Transitions in the neck
region are demonstrated, respectively, in the nonresonance, resonance, and degradation cases. One of the important contributions
of the paper is to derive necessary and sufficiency conditions for stability of the motion near the equilibria. Another contribution
is to demonstrate numerically that the critical KAM torus of nontransition is filled with the (1,1)-homoclinic orbits of the
Lyapunov orbit. 相似文献
4.
Roman V. Baluyev Konstantin V. Kholshevnikov 《Celestial Mechanics and Dynamical Astronomy》2005,91(3-4):287-300
In the paper by Kholshevnikov and Vassilie, 1999, (see also references therein) the problem of finding critical points of
the distance function between two confocal Keplerian elliptic orbits (hence finding the distance between them in the sense
of set theory) is reduced to the determination of all real roots of a trigonometric polynomial of degree eight. In non-degenerate
cases a polynomial of lower degree with such properties does not exist. Here we extend the results to all possible cases of
ordered pairs of orbits in the Two–Body–Problem. There are nine main cases corresponding to three main types of orbits: ellipse,
hyperbola, and parabola. Note that the ellipse–hyperbola and hyperbola–ellipse cases are not equivalent as we exclude the
variable marking the position on the second curve. For our purposes rectilinear trajectories can be treated as particular
(not limiting) cases of elliptic or hyperbolic orbits. 相似文献
5.
An analysis and interpretation of reflected solar Lyman α intensity data acquired with the Hubble Space Telescope (HST) implies
an equatorially confined atmosphere with SO2 column densities ∼ 1–2 × 1016 cm-2. Poleward of 30° the SO2 density must decrease sharply reaching an asymptotic polar value of < 1015 cm-2 at 45° to achieve the observed 2 kR intensity peaks. The corresponding surface reflectivities must be either a constant 0.047
for higher equatorial SO2 or a variable reflectivity of 0.027 with lower SO2 densities at the equator increasing to a polar value of ∼ 0.05. The average residence time for an atmospheric SO2 molecule is ∼ 2–3 days for the canonical mass loading rate of the Io plasma torus = 1030 amu s-1. With atomic hydrogen in the atmosphere and corona constrained by the HST observations, it is estimated that a pickup proton
density ratio of 0.25–0.4% can be sustained by a supply of Io plasma torus protons neutralized in Io's atmosphere/exosphere,
if protons constitute 7% of the total torus ion density, which is close to the Chust et al. (1999) pickup proton density ratio and under the widely quoted 10% proton content of the torus.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
6.
R. Sahai K. Young N. Patel C. Sánchez Contreras M. Morris 《Astrophysics and Space Science》2008,313(1-3):241-244
Using the Submillimeter Array (SMA), we have obtained high angular-resolution (∼1″) interferometric maps of the submillimeter
(0.88 mm) continuum and CO J=3–2 line from IRAS 22036+5306 (I 22036), a bipolar pre-planetary nebula (PPN) with knotty jets discovered in our HST SNAPshot
survey of young PPNe. In addition, we have obtained supporting lower-resolution (∼10″) 2.6 mm continuum and CO, 13CO J=1–0 observations with the Owens Valley Radio Observatory (OVRO) interferometer. We find an unresolved source of submillimeter
(and millimeter-wave) continuum emission in I 22036, implying a very substantial mass (0.02–0.04M
⊙) of large (i.e., radius ≳1 mm), cold (≲50 K) dust grains associated with I 22036’s toroidal waist. The CO J=3–2 observations show the presence of a very fast (∼220 km s−1), highly collimated, massive (0.03M
⊙) bipolar outflow with a very large scalar momentum (about 1039 g cm s−1), and the characteristic spatio-kinematic structure of bow-shocks at the tips of this outflow. The fast outflow in I 22036,
as in most PPNe, cannot be driven by radiation pressure. The large mass of the torus suggests that it has most likely resulted
from common-envelope evolution in a binary, however it remains to be seen whether or not the time-scales required for the
growth of grains to millimeter sizes in the torus are commensurate with such a formation scenario. The presence of the torus
should facilitate the formation of the accretion disk needed to launch the jet. We also find that the 13C/12C ratio in I 22036 is very high (0.16), close to the maximum value achieved in equilibrium CNO-nucleosynthesis (0.33). The
combination of the high circumstellar mass (i.e., in the torus and an extended dust shell inferred from ISO far-infrared spectra)
and the high 13C/12C ratio in I 22036 provides strong support for this object having evolved from a massive (≳4M
⊙) progenitor in which hot-bottom-burning has occurred. 相似文献
7.
Yuan Ren Pierpaolo Pergola Elena Fantino Bianca Thiere 《Celestial Mechanics and Dynamical Astronomy》2012,112(1):1-21
Over the past three decades, ballistic and impulsive trajectories between libration point orbits (LPOs) in the Sun–Earth–Moon
system have been investigated to a large extent. It is known that coupling invariant manifolds of LPOs of two different circular
restricted three-body problems (i.e., the Sun–Earth and the Earth–Moon systems) can lead to significant mass savings in specific
transfers, such as from a low Earth orbit to the Moon’s vicinity. Previous investigations on this issue mainly considered
the use of impulsive maneuvers along the trajectory. Here we investigate the dynamical effects of replacing impulsive ΔV’s with low-thrust trajectory arcs to connect LPOs using invariant manifold dynamics. Our investigation shows that the use
of low-thrust propulsion in a particular phase of the transfer and the adoption of a more realistic Sun–Earth–Moon four-body
model can provide better and more propellant-efficient solution. For this purpose, methods have been developed to compute
the invariant tori and their manifolds in this dynamical model. 相似文献
8.
Toshio Fukushima 《Celestial Mechanics and Dynamical Astronomy》1999,75(3):201-226
We developed a procedure to solve a modification of the standard form of the universal Kepler’s equation, which is expressed
as a nondimensional equation with respect to a nondimensional variable. After reducing the domain of the variable and the
argument by using the symmetry and the periodicity of the equation, the method first separates the case where the solution
is so small that it is given an inverted series. Second, it separates the cases where the elliptic, parabolic, or hyperbolic
standard forms of Kepler’s equation are suitable. Here the separation is done by judging whether detouring these nonuniversal
equations will cause a 1-bit loss of information to their nonuniversal solutions or not. Then the nonuniversal equations are
solved by the author’s procedures to solve the elliptic Kepler’s equation (Fukushima, 1997a), Barker’s equation (Fukushima,
1998), and the hyperbolic Kepler’s equation (Fukushima, 1997b), respectively. And their nonuniversal solutions are transformed
back to the solution of the universal equation. For the rest of the case, we obtain an approximate solution by solving roughly
the approximated cubic equation as we did in solving Barker’s equation. Then the correction to the approximate solution is
obtained by Halley’s method precisely. There the special function appeared in the universal equation is rewritten into a combination
of similar special functions of small arguments, so that they are efficiently evaluated by their Taylor series. Numerical
measurements showed that, in the case of Intel Pentium II processor, the new method is 10–25 times as fast as Shepperd’s method
(Shepperd, 1985) and 7–13 times as fast as the standard Newton method.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
Kathryn E. Davis Rodney L. Anderson Daniel J. Scheeres George H. Born 《Celestial Mechanics and Dynamical Astronomy》2011,109(3):241-264
This paper presents a method to construct optimal transfers between unstable periodic orbits of differing energies using invariant
manifolds. The transfers constructed in this method asymptotically depart the initial orbit on a trajectory contained within
the unstable manifold of the initial orbit and later, asymptotically arrive at the final orbit on a trajectory contained within
the stable manifold of the final orbit. Primer vector theory is applied to a transfer to determine the optimal maneuvers required
to create the bridging trajectory that connects the unstable and stable manifold trajectories. Transfers are constructed between
unstable periodic orbits in the Sun–Earth, Earth–Moon, and Jupiter-Europa three-body systems. Multiple solutions are found
between the same initial and final orbits, where certain solutions retrace interior portions of the trajectory. All transfers
created satisfy the conditions for optimality. The costs of transfers constructed using manifolds are compared to the costs
of transfers constructed without the use of manifolds. In all cases, the total cost of the transfer is significantly lower
when invariant manifolds are used in the transfer construction. In many cases, the transfers that employ invariant manifolds
are three times more efficient, in terms of fuel expenditure, than the transfer that do not. The decrease in transfer cost
is accompanied by an increase in transfer time of flight. 相似文献
10.
We prove the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic
invariant tori for (an “outer solar-system” model of) the planar (N + 1)-body problem.
相似文献
11.
N. Voglis G. Contopoulos C. Efthymiopoulos 《Celestial Mechanics and Dynamical Astronomy》1999,73(1-4):211-220
Two simple and efficient numerical methods to explore the phase space structure are presented, based on the properties of
the "dynamical spectra". 1) We calculate a "spectral distance" D of the dynamical spectra for two different initial deviation
vectors. D → 0 in the case of chaotic orbits, while D → const ≠ 0 in the case of ordered orbits. This method is by orders
of magnitude faster than the method of the Lyapunov Characteristic Number (LCN). 2) We define a sensitive indicator called
ROTOR (ROtational TOri Recongnizer) for 2D maps. The ROTOR remains zero in time on a rotational torus, while it tends to infinity
at a rate ∝ N = number of iterations, in any case other than a rotational torus. We use this method to locate the last KAM
torus of an island of stability, as well as the most important cantori causing stickiness near it.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
12.
Yi-Sui Sun Li-Yong Zhou Ji-Lin Zhou 《Celestial Mechanics and Dynamical Astronomy》2005,92(1-3):257-272
With the standard map model, we study the stickiness effect of invariant tori, particularly the role of hyperbolic sets in this effect. The diffusion of orbits originated from the neighborhoods of hyperbolic points, periodic islands and torus is studied. We find that they possess similar diffusion rules, but the diffusion of orbits originated from the neighborhood of a torus is faster than that originated near a hyperbolic set. The numerical results show that an orbit in the neighborhood of a torus spends most of time around hyperbolic invariant sets. We also calculate the areas of islands with different periods. The decay of areas with the periods obeys a power law, and the absolute values of the exponents increase monotonously with the perturbation parameter. According to the results obtained, we conclude that the stickiness effect of tori is caused mainly by the hyperbolic invariant sets near the tori, and the diffusion speed becomes larger when orbits diffuse away from the torus. 相似文献
13.
Due to the existence of invariant tori, chaotic sea and hyperbolic structures in higher dimensional phase space of a volume-preserving
map, the diffusion route of chaotic orbits will be complicated. The velocity of diffusion will be very slow if the orbits
are near an invariant torus. In order to realize this complicated diffusion phenomenon, in this paper we study the diffusion
characters in the different regions, i.e., chaotic, hyperbolic and invariant tori's regions. We find that for the three different
regions, the diffusion velocities are different. The diffusion velocity in the vicinity of an invariant torus is the slowest
one.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
14.
Toshio Fukushima 《Celestial Mechanics and Dynamical Astronomy》2009,105(4):305-328
As a preparation step to compute Jacobian elliptic functions efficiently, we created a fast method to calculate the complete
elliptic integral of the first and second kinds, K(m) and E(m), for the standard domain of the elliptic parameter, 0 < m < 1. For the case 0 < m < 0.9, the method utilizes 10 pairs of approximate polynomials of the order of 9–19 obtained by truncating Taylor series
expansions of the integrals. Otherwise, the associate integrals, K(1 − m) and E(1 − m), are first computed by a pair of the approximate polynomials and then transformed to K(m) and E(m) by means of Jacobi’s nome, q, and Legendre’s identity relation. In average, the new method runs more-than-twice faster than the existing methods including
Cody’s Chebyshev polynomial approximation of Hastings type and Innes’ formulation based on q-series expansions. Next, we invented a fast procedure to compute simultaneously three Jacobian elliptic functions, sn(u|m), cn(u|m), and dn(u|m), by repeated usage of the double argument formulae starting from the Maclaurin series expansions with respect to the elliptic
argument, u, after its domain is reduced to the standard range, 0 ≤ u < K(m)/4, with the help of the new method to compute K(m). The new procedure is 25–70% faster than the methods based on the Gauss transformation such as Bulirsch’s algorithm, sncndn, quoted in the Numerical Recipes even if the acceleration of computation of K(m) is not taken into account. 相似文献
15.
A model of the early universe in the Einstein theory of gravitation, supplemented by a conformalty invariant version of the
Weinberg—Salam model, is considered. The conformai symmetry principle leads to the need to eliminate the Higgs potential from
the expression for gravitational action, using the Lagrangian density of the model of Weinberg—Salam electroweak interactions
as the material source, and to incorporate the conformally invariant Penrose—Chernikov—Tagirov term. In the limit of flat
space, we arrive at the a version of the Weinberg—Salam model without Higgs particle-like excitations. In the conformalty
invariant model under consideration, Higgs fields are absorbed by the spatial metric, so one can assume that the masses of
elementary particles originate at the time when the evolution of the universe begins.
Translated from Astrofizika, Vol. 41, No. 3, pp. 459–471, July–September, 1998. 相似文献
16.
Sławomir Breiter 《Celestial Mechanics and Dynamical Astronomy》1998,71(4):229-241
An explicit symplectic integrator is constructed for perturbed elliptic orbits of an arbitrary eccentricity. The perturbation
should be Hamiltonian, but it may depend on time explicitly. The main feature of the integrator is the use of KS variables
in the ten-dimensional extended phase space. As an example of its application the motion of an Earth satellite under the action
of the planet's oblateness and of lunar perturbations is studied. The results confirm the superiority of the method over a
classical Wisdom–Holman algorithm in both accuracy and computation time.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
17.
An enlarged averaged Hamiltonian is introduced to compute several families of periodic orbits of the planar elliptic 3-body
problem, in the Sun–Jupiter–Asteroid system, near the 4:1 resonance. Four resonant critical point families are found and their
stability is studied. The families of symmetric periodic orbits of the elliptic problem appear near the corresponding fixed
points computed in this model. There is a good agreement for moderate eccentricity of the asteroid for three of these families,
whereas the remaining family cannot be considered as a family of periodic orbits of the real model.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
18.
E. Martínez-Gómez H. J. Durand-Manterola H. Pérez de Tejada 《Astrophysics and Space Science》2006,306(4):259-267
Voyager's plasma probe observations suggest that there are at least three fundamentally different plasma regimes in Saturn:
the hot outer magnetosphere, the extended plasma sheet, and the inner plasma torus. At the outer regions of the inner torus
some ions have been accelerated to reach energies of the order of 43 keV. We develop a model that calculates the acceleration
of charged particles in the Saturn's magnetosphere. We propose that the stochastic electric field associated to the observed
magnetic field fluctuations is responsible of such acceleration. A random electric field is derived from the fluctuating magnetic
field – via a Monte Carlo simulation – which then is applied to the momentum equation of charged particles seeded in the magnetosphere.
Taking different initial conditions, like the source of charged particles and the distribution function of their velocities,
we find that particles injected with very low energies ranging from 0.129 eV to 5.659 keV can be strongly accelerated to reach
much higher energies ranging from 22.220 eV to 9.711 keV as a result of 125,000 hitting events (the latter are used in the
numerical code to produce the particle acceleration over a predetermined distance). 相似文献
19.
Pavol Pástor Jozef Klačka Ladislav Kómar 《Celestial Mechanics and Dynamical Astronomy》2009,103(4):343-364
Effect of stellar electromagnetic radiation on the motion of spherical dust particle in mean motion orbital resonances with
a planet is investigated. Planar circular restricted three-body problem with the Poynting–Robertson (P–R) effect yields monotonic
secular evolution of eccentricity when the particle is trapped in the resonance. Planar elliptic restricted three-body problem
with the P–R effect enables nonmonotonous secular evolution of eccentricity and the evolution of eccentricity is qualitatively
consistent with the published results for the complicated case of interaction of electromagnetic radiation with nonspherical
dust grain. Thus, it is sufficient to allow either nonzero eccentricity of the planet or nonsphericity of the grain and the
orbital evolutions in the resonances are qualitatively equal for the two cases. This holds both for exterior and interior
mean motion orbital resonances. Evolutions of argument of perihelion in the planar circular and elliptical restricted three-body
problems are shown. Numerical integrations show that an analytic expression for the secular time derivative of the particle’s
argument of perihelion does not exist, if only dependence on semimajor axis, eccentricity and argument of perihelion is admitted.
Connection between the shift of perihelion and oscillations in secular eccentricity is presented for the planar elliptic restricted
three-body problem with the P–R effect. Period of the oscillations corresponds to the period of one revolution of perihelion.
Change of optical properties of the spherical grain with the heliocentric distance is also considered. The change of the optical
properties: (i) does not have any significant influence on the secular evolution of eccentricity, (ii) causes that the shift
of perihelion is mainly in the same direction/orientation as the particle motion around the Sun. The statements hold both
for circular and noncircular planetary orbits. 相似文献
20.
In this work we describe a technique developed to improve medium-term prediction methods of monthly smoothed sunspot numbers.
Each month, the predictions are updated using the last available observations (see the monthly output in real time at ). The improvement of the predictions is provided by applying an adaptive Kalman filter to the medium-term predictions obtained
by any other method, using the six-monthly mean values of sunspot numbers covering the six months between the last available
value of the 13-month running mean (the starting point for the predictions) and the “current time” (i.e. now). Our technique provides an effective estimate of the sunspot index at the current time. This estimate becomes the new
starting point for the updated prediction that is shifted six months ahead in comparison with the last available 13-month
running mean, and it provides an increase of prediction accuracy. Our technique has been tested on three medium-term prediction
methods that are currently in real-time operation: The McNish–Lincoln method (NGDC), the standard method (SIDC), and the combined
method (SIDC). With our technique, the prediction accuracy for the McNish–Lincoln method is increased by 17 – 30%, for the
standard method by 5 – 21% and for the combined method by 6 – 57%. 相似文献