共查询到20条相似文献，搜索用时 31 毫秒
1.
Rodolpho Vilhena de Moraes Regina Elaine Santos Cabette Maria Cecília Zanardi Teresinha J. Stuchi Jorge Kennety Formiga 《Celestial Mechanics and Dynamical Astronomy》2009,104(4):337-353
The stability of the rotational motion of artificial satellites is analyzed considering perturbations due to the gravity gradient
torque, using a canonical formulation, and Andoyer’s variables to describe the rotational motion. The stability criteria employed
requires the reduction of the Hamiltonian to a normal form around the stable equilibrium points. These points are determined
through a numerical study of the Hamilton’s equations of motion and linear study of their stability. Subsequently a canonical
linear transformation is used to diagonalize the matrix associated to the linear part of the system resulting in a normalized
quadratic Hamiltonian. A semi-analytic process of normalization based on Lie–Hori algorithm is applied to obtain the Hamiltonian
normalized up to the fourth order. Lyapunov stability of the equilibrium point is performed using Kovalev and Savchenko’s
theorem. This semi-analytical approach was applied considering some data sets of hypothetical satellites, and only a few cases
of stable motion were observed. This work can directly be useful for the satellite maintenance under the attitude stability
requirements scenario. 相似文献
2.
N. D. Caranicolas 《Journal of Astrophysics and Astronomy》2001,22(4):309-319
We present a map for the study of resonant motion in a potential made up of two harmonic oscillators with quartic perturbing
terms. This potential can be considered to describe motion in the central parts of non-rotating elliptical galaxies. The map
is based on the averaged Hamiltonian. Adding on a semi-empirical basis suitable terms in the unperturbed averaged Hamiltonian,
corresponding to the 1:1 resonant case, we are able to construct a map describing motion in several resonant cases. The map
is used in order to find thex − p
x
Poincare phase plane for each resonance. Comparing the results of the map, with those obtained by numerical integration of
the equation of motion, we observe, that the map describes satisfactorily the broad features of orbits in all studied cases
for regular motion. There are cases where the map describes satisfactorily the properties of the chaotic orbits as well. 相似文献
3.
We present a comparative study of low-l solar p-mode parameters extracted by genetic-algorithm and ‘standard’ hill-climbing minimisation routines. To effect this we make
use of observations made in integrated sunlight by the Birmingham Solar-Oscillations Network (BiSON) and the GOLF instrument
on board the ESA/NASA SOHO satellite, in addition to artificial data. We find that over the central part of the p-mode range the two fitting routines return similar results. However, at low frequencies — where the S/N in the modes is low
and their resonant peaks narrow — we find that the genetic routine appears to offer more robust estimates of the underlying
parameters. 相似文献
4.
We consider the Sitnikov problem; from the equations of motion we derive the approximate Hamiltonian flow. Then, we introduce
suitable action–angle variables in order to construct a high order normal form of the Hamiltonian. We introduce Birkhoff Cartesian
coordinates near the elliptic orbit and we analyze the behavior of the remainder of the normal form. Finally, we derive a
kind of local stability estimate in the vicinity of the periodic orbit for exponentially long times using the normal form
up to 40th order in Cartesian coordinates. 相似文献
5.
We have performed normalization of Hamiltonian in the generalized photogravitational restricted three body problem with Poynting–Robertson
drag. In this problem we have taken bigger primary as source of radiation and smaller primary as an oblate spheroid. Whittaker’s
method is used to transform the second order part of the Hamiltonian into the normal form.
相似文献
6.
In this paper, we use a semi-analytical approach to analyze the global structure of the phase space of the planar planetary 3/1 mean-motion resonance. The case where the outer planet is more massive than its inner companion is considered. We show that the resonant dynamics can be described using two fundamental parameters, the total angular momentum and the spacing parameter. The topology of the Hamiltonian function describing the resonant behaviour is investigated on a large domain of the phase space without time-expensive numerical integrations of the equations of motion, and without any restriction on the magnitude of the planetary eccentricities. The families of the Apsidal Corotation Resonances (ACR) parameterized by the planetary mass ratio are obtained and their stability is analyzed. The main dynamical features in the domains around the ACR are also investigated in detail by means of spectral analysis techniques, which allow us to detect the regions of different regimes of motion of resonant systems. The construction of dynamical maps for various values of the total angular momentum shows the evolution of domains of stable motion with the eccentricities, identifying possible configurations suitable for exoplanetary systems. 相似文献
7.
Any dynamical system can be put in generalized canonical form through the introduction of a set of auxiliary ‘conjugate’ variables
or momenta and solved by perturbation theory based on Lie series. The application of Hori's method for generalized canonical
system leads to a new canonical transformation — the Mathieu transformation — defined by the solution of the Hori auxiliary
system. This new transformation simplifies the algorithm since the inversion of the solution of the Hori auxiliary system
is no longer necessary. In this paper, we wish to show some peculiarities of this technique. 相似文献
8.
Alessandra Celletti Fabrizio Paita Giuseppe Pucacco 《Celestial Mechanics and Dynamical Astronomy》2018,130(2):15
We study the dynamics of the de Sitter resonance, namely the stable equilibrium configuration of the first three Galilean satellites. We clarify the relation between this family of configurations and the more general Laplace resonant states. In order to describe the dynamics around the de Sitter stable equilibrium, a one-degree-of-freedom Hamiltonian normal form is constructed and exploited to identify initial conditions leading to the two families. The normal form Hamiltonian is used to check the accuracy in the location of the equilibrium positions. Besides, it gives a measure of how sensitive it is with respect to the different perturbations acting on the system. By looking at the phase plane of the normal form, we can identify a Laplace-like configuration, which highlights many substantial aspects of the observed one. 相似文献
9.
We have extend Stormer’s problem considering four magnetic dipoles in motion trying to justify the phenomena of extreme “orderlines”
such as the ones observed in the rings of Saturn; the aim is to account the strength of the Lorentz forces estimating that
the Lorentz field, co-acting with the gravity field of the planet, will limit the motion of all charged particles and small
size grains with surface charges inside a layer of about 200 m thickness as that which is observed in the rings of Saturn.
For this purpose our interest feast in the motion of charged particles with neglected mass where only electromagnetic forces
accounted in comparison to the weakness of the Newtonian fields. This study is particularly difficult because in the regions
we investigate these motions there is enormous three dimensional instability. Following the Poincare’s hypothesis that periodic
solutions are ‘dense’ in the set of all solutions in Hamiltonian systems we try to calculate many families of periodic solutions
and to study their stability. In this work we prove that in this environment charged particles can trace planar symmetric
periodic orbits. We discuss these orbits in details and we give their symplectic relations using the Hamiltonian formulation
which is related to the symplectic matrix. We apply numerical procedures to find families of these orbits and to study their
stability. Moreover we give the bifurcations of these families with families of planar asymmetric periodic orbits and families
of three dimensional symmetric periodic orbits. 相似文献
10.
Badam Singh Kushvah 《Astrophysics and Space Science》2009,323(1):57-63
Linearization of the Hamiltonian is being performed in the generalized photogravitational Chermnykh’s problem. The normal
form of the second order part of the Hamiltonian have been found. The effect of radiation pressure, gravitational potential
from the belt have been examined analytically and numerically 相似文献
11.
The regularization of a new problem, namely the three-body problem, using ‘similar’ coordinate system is proposed. For this
purpose we use the relation of ‘similarity’, which has been introduced as an equivalence relation in a previous paper (see
Roman in Astrophys. Space Sci. doi:, 2011). First we write the Hamiltonian function, the equations of motion in canonical form, and then using a generating function,
we obtain the transformed equations of motion. After the coordinates transformations, we introduce the fictitious time, to
regularize the equations of motion. Explicit formulas are given for the regularization in the coordinate systems centered
in the more massive and the less massive star of the binary system. The ‘similar’ polar angle’s definition is introduced,
in order to analyze the regularization’s geometrical transformation. The effect of Levi-Civita’s transformation is described
in a geometrical manner. Using the resulted regularized equations, we analyze and compare these canonical equations numerically,
for the Earth-Moon binary system. 相似文献
12.
R. A. Howland 《Celestial Mechanics and Dynamical Astronomy》1988,45(1-3):207-211
A new approach to the librational solution of the Ideal Resonance Problem has been devised--one in which a non-canonical transformation is applied to the classical Hamiltonian to bring it to the form of the simple harmonic oscillator. Although the traditional form of the canonical equations of motion no longer holds, a quasi-canonical form is retained in this single-degree-of-freedom system, with the customary equations being multiplied by a non-constant factor. While this makes the resulting system amenable to traditional transformation techniques, it must then be integrated directly. Singularities of the transformation in the circulation region limit application of the method to the librational region of motion.Computer-assisted algebra has been used in all three stages of the solution to fourth order of this problem: using a general-purpose FORTRAN program for the quadratic analytical solution of Hamiltonians in action-angle variables, the initial transformation is carried out by direct substitution and the resulting Hamiltonian transformed to eliminate angular variables. The resulting system of differential equations, requiring the expected elliptic functions as part of their solution, is currently in the process of being integrated using the LISP-based REDUCE software, by programming the required recursive rules for elliptic integration.Basic theory of this approach and the computer implementation of all these techniques is described. Extension to higher order of the solution is also discussed. 相似文献
13.
Andre Deprit 《Celestial Mechanics and Dynamical Astronomy》1976,13(2):253-263
Cartan's exterior calculus is used to refer a perturbed Keplerian motion to an ideal frame by means of either the Eulerian parameters or the Eulerian angles, in which case the equations are given a Hamiltonian form. The results are compared with the corresponding systems in the orbital and nodal frames. 相似文献
14.
This paper presents a Hamiltonian approach to modelling spacecraft motion relative to a circular reference orbit based on
a derivation of canonical coordinates for the relative state-space dynamics. The Hamiltonian formulation facilitates the modelling
of high-order terms and orbital perturbations within the context of the Clohessy–Wiltshire solution. First, the Hamiltonian
is partitioned into a linear term and a high-order term. The Hamilton–Jacobi equations are solved for the linear part by separation,
and new constants for the relative motions are obtained, called epicyclic elements. The influence of higher order terms and
perturbations, such as Earth’s oblateness, are incorporated into the analysis by a variation of parameters procedure. As an
example, closed-form solutions for J2-invariant orbits are obtained. 相似文献
15.
This note gives a concise algorithm for computing a normal form for a real linear Hamiltonian differential equatin which has purely imaginary eigenvalues. This algorithm is then applied to the differential equation which comes from the quadratic terms of the Hamiltonian of the restricted three body problem at a Lagrange equilateral triangle equilibrium point. 相似文献
16.
The properties of the magnetostatic structures in a collisionless relativistic plasma found by exactly solving the nonlinear
self-consistent kinetic and Maxwell equations using the method of invariants of particle motion are analyzed. These structures
include individual neutral current sheets and cylindrically symmetric filaments as well as their ensembles, admitting a wide
variety of types of particle energy distribution functions. Relationships are established between the possible parameters
of the current sheets and filaments—their sizes, currents and magnetic fields, and the degree of anisotropy of the particle
momentum distribution. The extent to which these parameters are conditioned by the properties of the Weibel instability that
can produce these structure is also discussed. The spectral peculiarities of the synchrotron radiation from the particles
that form the current sheets and filaments are investigated in the special case of power-law energy distribution functions. 相似文献
17.
John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》1982,27(3):305-322
The factors which affect the linear stability of a periodic planetary orbit in the plane are studied. It is proved that planetary systems with two planets describing nearly circular orbits in the same direction are linearly stable and no perturbation exists which destroys the stability, unless a resonance of the form 1/3, 3/5, 5/7, ... among the orbits of the planets occurs. This latter resonant case is always unstable. Retrograde motion is always linearly stable. Planetary systems with three or more planets in nearly circular orbits in the same direction are proved to be unstable, in the sense that a Hamiltonian perturbation always exists which destroys the stability. The generation of instability in the case of three or more planets is not only due to the existence of resonances, as in the case of two planets, but also to the nonexistence of integrals of motion, apart from the energy and angular momentum integrals. It is also proved that planetary systems with nearly elliptic orbits of the planets are unstable. 相似文献
18.
The post-Newtonian mean anomaly advance as further post-Keplerian parameter in pulsar binary systems
Lorenzo Iorio 《Astrophysics and Space Science》2007,312(3-4):331-335
The post-Newtonian gravitoelectric secular rate of the mean anomaly ℳ is worked out for a two-body system in the framework
of the General Theory of Relativity. The possibility of using such an effect, which is different from the well known decrease
of the orbital period due to gravitational wave emission, as a further post-Keplerian parameter in binary systems including
at least one pulsar is examined. The resulting effect is almost three times larger than the periastron advance
. E.g., for the recently discovered double pulsar system PSR J0737-3039 A+B it would amount to −47.79 deg yr−1. This implies that it could be extracted from the linear part of a quadratic fit of the orbital phase because the uncertainties
both in the linear drift due to the mean motion and in the quadratic shift due to the gravitational wave are smaller. The
availability of such additional post-Keplerian parameter would be helpful in further constraining the General Theory of Relativity,
especially for such systems in which some of the other post-Keplerian parameters can be measured with limited accuracy. Moreover,
also certain pulsar-white dwarf binary systems, characterized by circular orbits like PSR B1855+09 and a limited number of
measured post-Keplerian parameters, could be used for constraining competing theories of gravity. 相似文献
19.
Giuseppe Pucacco 《New Astronomy》2012,17(5):475-482
We compute the normal forms for the Hamiltonian leading to the epicyclic approximations of the (perturbed) Kepler problem in the plane. The Hamiltonian setting corresponds to the dynamics in the Hill synodic system where, by means of the tidal expansion of the potential, the equations of motion take the form of perturbed harmonic oscillators in a rotating frame. In the unperturbed, purely Keplerian case, the post-epicyclic solutions produced with the normal form coincide with those obtained from the expansion of the solution of the Kepler equation. In all cases where the perturbed problem can be cast in autonomous form, the solution is easily obtained as a perturbation series. The generalization to the spatial problem and/or the non-autonomous case is straightforward. 相似文献
20.
It is demonstrated that, at high rigidities (50 GV and beyond), all the main features of cosmic-ray anisotropy of solar origin
can be explained in terms of regular particle motion —without diffusion being involved — in the large-scale interplanetary
magnetic field (IMF). A simple model of the IMF is adopted with a corotating warped neutral sheet separating the regions of
alternative polarities; the warped shape is indispensable for obtaining any form of anisotropy. Energy losses occurring along
various computed trajectories are calculated to give the sidereal, solar and antisidereal intensity waves. The reliability
of the variations obtained are checked by changing the parameters of the IMF model. Both the sense and amplitude of the polarity-dependent
sidereal vector are compatible with those established experimentally. Also reproduced are the predictions of corotation in
addition to the 3-hour phase of the semi-diurnal wave. The corotation is found to be near perfect at 50 GV, while it reduces
at 100 GV. The model presented accounts for the change of solar daily vector that was observed in 1969. 相似文献