共查询到20条相似文献，搜索用时 46 毫秒
1.
Andrzej J. Maciejewski Maria Przybylska Leon Simpson Wojciech Szumiński 《Celestial Mechanics and Dynamical Astronomy》2013,117(3):315-330
This paper discusses a constrained gravitational three-body problem with two of the point masses separated by a massless inflexible rod to form a dumbbell. This problem is a simplification of a problem of a symmetric rigid body and a point mass, and has numerous applications in Celestial Mechanics and Astrodynamics. The non-integrability of this system is proven. This was achieved thanks to an analysis of variational equations along a certain particular solution and an investigation of their differential Galois group. Nowadays this approach is the most effective tool for study integrability of Hamiltonian and non-Hamiltonian systems. 相似文献
2.
Determination of Stellar Parameters with GAIA 总被引：1，自引：0，他引：1
C.A.L. Bailer-Jones 《Astrophysics and Space Science》2002,280(1-2):21-29
The GAIA Galactic survey satellite will obtain photometry in 15 filters of over 109 stars in our Galaxy across a very wide range of stellar types. No other planned survey will provide so much photometric information
on so many stars. I examine the problem of how to determine fundamental physical parameters (T
eff, log g, [Fe/H] etc.) from these data. Given the size, multidimensionality and diversity of this dataset, this is a challenging task
beyond any encountered so far in large-scale stellar parametrization. I describe the problems faced (initial object identification,
interstellar extinction, multiplicity, missing data etc.) and present a framework in which they can be addressed. A probabilistic
approach is advocated on the grounds that it can take advantage of additional information (e.g. priors and data uncertainties)
in a consistent and useful manner, as well as give meaningful results in the presence of poor or degenerate data. Furthermore,
I suggest an approach to parametrization which can use the other information GAIA will acquire, in particular the parallax,
which has not previously been available for large-scale multidimensional parametrization. Several of the problems identified
and ideas suggested will be relevant to other large surveys, such as SDSS, DIVA,FAME, VISTA and LSST, as well as stellar parametrization
in a virtual observatory.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
3.
Frank H. Ditto 《Celestial Mechanics and Dynamical Astronomy》1969,1(1):130-140
The Peano-Baker method is applied to the integration of the variational equations to produce the partial derivatives used in satellite navigation. In this method the analytic form of the state transition partial derivatives can be factored so that numerical integration is applied only to the departures from a simplified analytical model.The advantage of using the Peano-Baker approach rather than direct integration of the variational equations is that with the Peano-Baker method numerical integration can be performed adequately with low order formulae and relatively large step sizes. Numerical results are indicated. 相似文献
4.
The formulas for the Poisson bracket of a perturbed two-body problem and a perturbed planetary problem are found in different systems of Keplerian elements. As with canonical parametrization, the Poisson bracket is equal to a linear combination of partial brackets, but it contains coefficients depending on semimajor axis, eccentricity, and inclination. A simple relation between the Poisson brackets and matrices of coefficients of Lagrange-type equations determining the variations of osculating elements is derived. The Poisson bracket of D'Alembertian functions is proved to be a D'Alembertian one by itself. 相似文献
5.
Seokcheon Lee 《Astrophysics and Space Science》2014,350(2):785-790
The absence of compelling theoretical model requires the parameterizing the dark energy to probe its properties. The parametrization of the equation of state of the dark energy is a common method. We explore the theoretical optimization of the parametrization based on the Fisher information matrix. As a suitable parametrization, it should be stable at high redshift and should produce the determinant of the Fisher matrix as large as possible. For the illustration, we propose one parametrization which can satisfy both criteria. By using the proper parametrization, we can improve the constraints on the dark energy even for the same data. We also show the weakness of the so-called principal component analysis method. 相似文献
6.
A. G. Mavraganis 《Celestial Mechanics and Dynamical Astronomy》1981,23(3):287-293
The author's aim is to study in this paper the stationary state of the planar Magnetic-Binary problem by taking into consideration the oblateness of the more massive primary, and then to investigate the stability of motion about the equilibrium points by means of the characteristic polynomial of the linearised variational equations. 相似文献
7.
H. J. Peng Q. Gao Z. G. Wu W. X. Zhong 《Celestial Mechanics and Dynamical Astronomy》2011,110(4):319-342
In this paper, from a Hamiltonian point of view, the nonlinear optimal control problems are transformed into nonlinear two-point
boundary value problems, and a symplectic adaptive algorithm based on the dual variational principle is proposed for solving
the nonlinear two-point boundary value problem. The state and the costate variables within a time interval are approximated
by using the Lagrange polynomial and the costate variables at two ends of the time interval are taken as independent variables.
Then, based on the dual variational principle, the nonlinear two-point boundary value problems are replaced by a system of
nonlinear equations which can preserve the symplectic structure of the nonlinear optimal control problem. Furthermore, the
computational efficiency of the proposed symplectic algorithm is improved by using the adaptive multi-level iteration idea.
The performance of the proposed algorithm is tested by the problems of Astrodynamics, such as the optimal orbital rendezvous
problem and the optimal orbit transfer between halo orbits. 相似文献
8.
S. Terracini 《Celestial Mechanics and Dynamical Astronomy》2006,95(1-4):3-25
This expository paper gathers some of the results obtained by the author in recent works in collaboration with Davide Ferrario and Vivina Barutello, focusing on the periodic n-body problem from the perspective of the calculus of variations and minimax theory. These researches were aimed at developing a systematic variational approach to the equivariant periodic n-body problem in the two and three-dimensional space. The purpose of this paper is to expose the main problems and achievements of this approach. The material here was exposed in the talk that given at the Meeting CELMEC IV promoted by SIMCA (Società italiana di Meccanica Celeste). 相似文献
9.
Sandro da Silva Fernandes 《Celestial Mechanics and Dynamical Astronomy》2003,87(3):307-315
In this paper the new approach for the integration theory of the canonical version of Hori method recently proposed is extended to the non-canonical one. It will be shown that the non-homogeneous ordinary differential equation with an auxiliary parameter t* associated with the mth order equation of the algorithm can also be replaced by a non-homogeneous partial differential equation in the time t. Using a generalized canonical approach, the general algorithm proposed by Sessin is then revised; as well as the Lagrange variational equations for the non-canonical version of Hori method. A simplified algorithm derived from Sessin's algorithm is presented for non-linear oscillations problem. 相似文献
10.
M. H. Haggag 《Astrophysics and Space Science》1985,115(1):155-161
The problem of particle reflection and transmission through slabs, which scatters isotropically, is analytically investigated. The solution is based on a projectional procedure, equivalent to a variational approach. Expressions for the reflection and transmission functions are given. Numerical results concern the above mentioned physical quantities are given and compared with the data available in literature. 相似文献
11.
Mayer's variational problem for a point with a limited mass flow rate is described by differential equations of the fourteenth order, allowing for a few first integrals. By reducing the equations to closed canonical form, these integrals are analyzed from the viewpoint of finding a possible solution to the problem via quadratures on zero, intermediate, and maximum thrust sections. In addition to confirming well-known cases of total integrability, this approach enabled us to establish that the essential difficulty of the solution of the space problem with intermediate thrust is reduced to finding one integral, and the solution of the problem with maximum thrust requires two integrals in involution. It is shown that these integrals can be applied to find particular solutions. 相似文献
12.
A first-order minimum propellant guidance law is developed for multi-impulse trajectories in an inverse-square gravitational field. A second-order variational analysis is used to formulate the guidance problem as an accessory minimum problem, i.e. minimize a quadratic form (second-variation in propellant consumption) subject to linear constraints (variational equations of motion and deterministic boundary conditions). Solution of the accessory minimum problem provides the optimal guidance law in feedback form. It is emphasized that this analysis takes into account the nominal impulse programme when calculating the optimal guidance corrections. It is shown that for multi-impulse transfers it is in general, non-optimal to add impulses. All corrections to the trajectory should be made by a combination of small changes in timing, magnitude and direction of the nominal impulses. 相似文献
13.
We discuss the question whether the way of finding the conservation laws based on variational formalism is applicable to the
multilevel problems of radiative transfer in a homogeneous atmosphere. For expository reasons, the simplest one-dimensional
model case is considered. For the special three-level problem treated in the paper the Lagrangian approach allows one to derive
not only the H- and K-integrals, but also the nonlinear integral which is an analog of the Q-integrals previously obtained
for the classical transfer problems. It is shown that, in general, the constraints imposed by the variational principle on
the symmetry properties of the transfer equations are too stringent to be satisfied.
Translated from Astrofizika, Vol. 42, No. 2, pp. 235–252, April–June, 1999. 相似文献
14.
V. V. Markellos 《Astrophysics and Space Science》1976,43(2):449-458
The stability parametersa, b, c, d of plane symmetric periodic solutions of non-integrable dynamical systems of two degrees of freedom are obtained in terms of their initial states of motion and elements of their variational matrics. Explicit formulae are given in the cases of the Störmer problem and the restricted problem of three bodies. 相似文献
15.
T. S. Boronenko 《Celestial Mechanics and Dynamical Astronomy》2017,127(2):139-161
In this article, we present the Lie transformation algorithm for autonomous Birkhoff systems. Here, we are referring to Hamiltonian systems that obey a symplectic structure of the general form. The Birkhoff equations are derived from the linear first-order Pfaff–Birkhoff variational principle, which is more general than the Hamilton principle. The use of 1-form in formulating the equations of motion in dynamics makes the Birkhoff method more universal and flexible. Birkhoff’s equations have a tensorial character, so their form is independent of the coordinate system used. Two examples of normalization in the restricted three-body problem are given to illustrate the application of the algorithm in perturbation theory. The efficiency of this algorithm for problems of asymptotic integration in dynamics is discussed for the case where there is a need to use non-canonical variables in phase space. 相似文献
16.
We analyze the stability of periodic solutions for Hill’s double-averaged problem by taking into account a central planet’s oblateness. They are generated by steady-state solutions that are stable in the linear approximation. By numerically calculating the monodromy matrix of variational equations, we plot its trace against the integral of the problem—an averaged perturbing function, for two model systems, [(Sun + Moon)-Earth-satellite] and (Sun-Uranus-satellite). We roughly estimate the ranges of values for the parameters of satellite orbits corresponding to periodic solutions of the evolutionary system that are stable in the linear approximation. 相似文献
17.
During the last three decades an observational approach has been applied at the Byurakan Astrophysical Observatory to the problems of the evolution of astronomical bodies and systems. In contradiction to the traditional point of view, assuming that the processes of condensation are dominant in the Universe, this approach makes use of the observed predominance of expansions, ejections, and explosions.In the past, the observational approach has led to the prediction of an expansion of some stellar associations confirmed later by the analysis of observations. It became clear that the stellar associations are very young systems where the star-formation process is still continuing. The new approach has also led to the concept of the activity of galactic nuclei. The observational approach considers as a phenomenon of primary importance the formation of nebulae as a consequence of the activity of dense bodies (nebulae surrounding the novae, planetary nebulae, supernova remnants, cometary nebulae, and the diffuse nebulae in OB-associations).The new approach in application to the early stages of stellar evolution is discussed. The T Tauri-stage is considered as a phase following the more dense protostellar state. The flare stars are regarded as the next phase of evolution. The phenomena of fuors (FU Ori-type brightenings) can be considered as an expression of the same tendency (the transformation of dense matter into a rarefied state). 相似文献
18.
A new approach is presented for the problem of planar optimal impulsive rendezvous of a spacecraft in an inertial frame near
a circular orbit in a Newtonian gravitational field. The total characteristic velocity to be minimized is replaced by a related
characteristic-value function and this related optimization problem can be solved in closed form. The solution of this problem
is shown to approach the solution of the original problem in the limit as the boundary conditions approach those of a circular
orbit. Using a form of primer-vector theory the problem is formulated in a way that leads to relatively easy calculation of
the optimal velocity increments. A certain vector that can easily be calculated from the boundary conditions determines the
number of impulses required for solution of the optimization problem and also is useful in the computation of these velocity
increments. Necessary and sufficient conditions for boundary conditions to require exactly three nonsingular non-degenerate
impulses for solution of the related optimal rendezvous problem, and a means of calculating these velocity increments are
presented. A simple example of a three-impulse rendezvous problem is solved and the resulting trajectory is depicted. Optimal
non-degenerate nonsingular two-impulse rendezvous for the related problem is found to consist of four categories of solutions
depending on the four ways the primer vector locus intersects the unit circle. Necessary and sufficient conditions for each
category of solutions are presented. The region of the boundary values that admit each category of solutions of the related
problem are found, and in each case a closed-form solution of the optimal velocity increments is presented. Similar results
are presented for the simpler optimal rendezvous that require only one-impulse. For brevity degenerate and singular solutions
are not discussed in detail, but should be presented in a following study. Although this approach is thought to provide simpler
computations than existing methods, its main contribution may be in establishing a new approach to the more general problem. 相似文献
19.
The planar isosceles three-body problem where the two symmetric bodies have small masses is considered as a perturbation of
the Kepler problem. We prove that the circular orbits can be continued to saddle orbits of the Isosceles problem. This continuation
is not possible in the elliptic case. Their perturbed orbits tend to a continued circular one or approach a triple collision.
The basic tool used is the study of the Poincaré maps associated with the periodic solutions.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
20.
We develop a new thermodynamic approach to the problem of the last stages of star formation, when a collapsing fragment evolves adiabatically into its final state: single protostar, surrounded or not by protoplanetary disc, or binary system. In this context, we point out the crucial role of the angular momentum transfer: a very efficient mechanism tends to form double stars with small mass secondaries, while a total decoupling yields twin binaries. Intermediate assumptions allow the birth of both kinds of binary systems, as well as the formation of not very massive protoplanetary discs. Discs of larger mass, which would be required to produce protoplanetary systems as a consequence of dynamical instabilities, do not form under any circumstances. A representation of the outcomes as functions of the corresponding initial conditions on the usual – plane gives well definite regions for single stars, protoplanetary discs, unbalanced systems and twin binaries. On this ground, a preliminary estimate of the percentage of stars surrounded by planetary systems is possible. A particular numerical simulation confirms the bimodality of the mass ratio distribution as well as the main features of the – plane partition. A few suggestions about non-adiabatic effects are also given. Our thermodynamic approach, supported by the numerical one and by the analysis of the observational statistics, allow to define a first unitary sketch for the formation of binary systems and protoplanetary discs. 相似文献