共查询到20条相似文献，搜索用时 31 毫秒
1.
Jacques Laskar 《Celestial Mechanics and Dynamical Astronomy》2017,128(4):475-482
Andoyer variables are well known for the study of rotational dynamics. These variables were derived by Andoyer through a procedure that can be also used to obtain the Hill variables of the Kepler problem. Andoyer construction can also forecast the Delaunay variables which canonicity is then obtained without the use of a generating function. 相似文献
2.
Cl. Froeschlé T.J. Jopek G.B. Valsecchi 《Celestial Mechanics and Dynamical Astronomy》1999,73(1-4):55-64
A set of geocentric variables suitable for the identification of meteoroid streams has been recently proposed and successfully
applied to photographic meteor orbits. We describe these variables and the secular invariance of some of them, and discuss
their use to improve the search for meteoroid stream parents.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
3.
R. Broucke 《Celestial Mechanics and Dynamical Astronomy》1978,18(3):207-222
In this article we study a form of equations of motion which is different from Lagrange's and Hamilton's equations: Pfaff's equations of motion. Pfaff's equations of motion were published in 1815 and are remarkably elegant as well as general, but still they are much less well known. Pfaff's equations can also be considered as the Euler-Lagrange equations derived from the linear Lagrangian rather than the usual Lagrangian which is quadratic in the velocity components. The article first treats the theory of changes of variables in Pfaff's equations and the connections with canonical equations as well as canonical transformations. Then the applications to the perturbed two-body problem are treated in detail. Finally, the Pfaffians are given in Hill variables and Scheifele variables. With these two sets of variables, the use of the true anomaly as independent variable is also considered. 相似文献
4.
It is shown that it is possible to make a change of variables in a Lagrangian in such a way that the number of variables is increased. The Euler-Lagrange equations in the redundant variables are obtained in the standard way (without the use of Lagrange Multipliers!). These equations are not independent but they are all valid and consistent. In some cases they are simpler than if the minimum number of variables are used. The redundant variables are supposed to be related to each other by several constraints (not necessarily holonomic), but these constraints are not used in the derivation of the equations of motion. The method is illustrated with the well known Kustaanheimo-Stiefel Regularization. Some interesting applications to perturbation theory are also described.The present research was carried out partially at the University of California and partially at the Jet Propulsion Laboratory under contract NAS7-100 with NASA.Presently Visiting Associate Professor at the University of Texas. 相似文献
5.
Starting values for the iterative solution of Kepler's equation are considered for hyperbolic orbits, and for generalized versions of the equation, including the use of universal variables. 相似文献
6.
J. M. A. Danby 《Celestial Mechanics and Dynamical Astronomy》1987,40(3-4):303-312
Recently proposed methods of iteration and initial guesses are discussed, including the method of Laguerre-Conway. Tactics for a more refined initial guess for use with universal variables over a small time interval are described. 相似文献
7.
In this paper, we make use of the Stumpff's functions to solve the problem of determining the orbit of a visual binary star in universal variables. The method is thus valid for all types of orbits: hyperbolic, parabolic and elliptic. 相似文献
8.
For use in numerical studies of rotational motion, a set of elements is introduced for the torque-free rotational motion of a rigid body around its barycenter. The elements are defined as the initial values of a modification of the Andoyer canonical variables. A computational procedure is obtained for determining these elements from the combination of the spin angular momentum vector and a triad defining the orientation of the rigid body. A numerical experiment shows that the errors of transformation between the elements and variables are sufficiently small. The errors increase linearly with time for some elements and quadratically for some others. 相似文献
9.
In this work, some numerical solutions of magnetohydrodynamic equations are investigated in the presence of radial and azimuthal components of magnetic field with the use of previously developed algorithm. In this algorithm, the thin shell approximation and a special separation of variables is used to obtain the radial and latitudinal variations of physical parameters in spherical coordinates. The solutions are obtained via this separation of variables in the components of momentum transfer equation. The analysis yields three important parameters which are the sphericity, density and radial components shape parameters in the latitudinal distributions of physical variables. The magnetic field profile, used here, produces comparable magnetic fluxes found in previous works. There is a considerable change in density with respect to reference model. Other physical parameters also reveal important physical results. It is as well shown that the spherical symmetric distributions of physical parameters are broken for the region of study. 相似文献
10.
L. Losco 《Celestial Mechanics and Dynamical Astronomy》1976,13(4):413-419
Résumé Une régularisation des collisions binaires du probléme desn corps est obtenue pour le probléme plan ou spatial par l'utilisation de la projection stéréographique de Moser en variables de Lagrange.
Regularization of binary collisions in the problem ofn-bodies is obtained for the plane or spatial problem, by use of Moser's stereographic mapping in Langrange's variables.相似文献
11.
Wagner Sessin 《Celestial Mechanics and Dynamical Astronomy》1986,39(2):173-180
In this paper a method for the integration of the equations of the extended Delaunay method is proposed. It is based on the equations of the characteristic curves associated with the partial differential equation of Delaunay-Poincaré. The use of the method of characteristics changes the partial differential equation for higher order approximations into a system of ordinary differential equations. The independent variable of the equations of the characteristics is used instead of the angular variables of the Jacobian methods and the averaging principle of Hori is applied to solve the equations for higher orders. It is well known that Jacobian methods applied to resonant problems generally lead to the singularity of Poincaré. In the ideal resonance problem, this singularity appears when higher order approximations of the librational motion are considered. The singularity of Poincaré is non-essential and is caused by the choice of the critical arguments as integration variables. The use of the independent variable of the equation of the characteristics in the place of the critical angles eliminates the singularity of Poincaré. 相似文献
12.
We eliminate by the method of von Zeipel the short-period terms in a first order-with respect to planetary masses—general planetary Uranus-Neptune theory. We exclude in the expansion terms of eccentricities and sines of inclinations higher than the third power.Our variables are the Poincaré canonical variables. We use the Jacobi-Radau set of origins, and we refer the planes of the osculating ellipses to a common fixed plane, the longitudes to a common origin. The short-periodic terms arising from the indirect and principal parts of the disturbing functions, are eliminated separately. The Fourier series of the principal part of the disturbing function, is reduced to the sum of only the first three terms. 相似文献
13.
The procedure of numerical integration of the elliptic three dimensional restricted threebody problem by the use of recurrence relations to evaluate successively higher derivatives of the relative position and velocity vectors of the bodies and of the variational matrix is investigated. A set of recurrence relations is developed which involves the introduction of fewer auxiliary variables than in previous papers of this series, while the recurrence relations themselves are of a simpler form than those in other treatments involving the same number of such auxiliary variables. A technique for automatic adjustment of the integration step-length at each point in the orbit, such that the local truncation error remains close to, but always less than, some specified amount, is incorporated. This technique involves the comparison of pre-integration values with those obtained after consecutive forward and reverse integration steps, and has decided advantages over step-adjustment methods currently in use.Both these modifications to previous techniques are shown, by presentation of sample computational results, to represent considerable savings in machine time for a given calculation and desired accuracy; these savings are generally around a factor of two and become greater as the desired accuracy in the computations increases. 相似文献
14.
M. S. Ruderman 《Solar physics》2017,292(8):111
We study the excitation of fluting perturbations in a magnetic tube by an initially imposed kink mode. We use the ideal magnetohydrodynamic (MHD) equations in the cold-plasma approximation. We also use the thin-tube approximation and scale the dependent and independent variables accordingly. Then we assume that the dimensionless amplitude of the kink mode is small and use it as an expansion parameter in the regular perturbation method. We obtain the expression for the tube boundary perturbation in the second-order approximation. This perturbation is a superposition of sausage and fluting perturbations. The amplitude of the fluting perturbation takes its maximum at the middle of the tube, and it monotonically decreases with the distance from the middle of the tube. 相似文献
15.
A complete analytical dynamic theory for the motion of Nereid has been constructed, accurate to approximately 0.01 arc second over several hundred years. The solution uses the Lie transform approach advanced by Deprit and is consistent with respect to the magnitudes of the disturbing functions, including all perturbations to an accuracy of 10–8 relative to the two-body potential (oblateness and third-body). Multiple short-period variables in the third-body perturbations are related via the ratio of their mean motions, reducing the number of independent variables. Extensive use is made of expansions giving trigonometric functions of the true anomaly as analytical Fourier series in the mean anomaly. Initial constants and mass parameters come from the data obtained during the Voyager II encounter with Neptune in 1989. 相似文献
16.
The Tycho Epoch Photometry Annex A, a data base of photometry of more than 34 000 bright stars, has been searched for periodic variable stars with approximately sinusoidal light curves. Advantage was taken of special properties of the observing programme (photometry in two wavebands, availability of repeated measurements) to use simple but efficient variable selection criteria. Details of 70 strong candidate variables are presented. 相似文献
17.
P. J. Message 《Celestial Mechanics and Dynamical Astronomy》1987,43(1-4):119-125
In the presence of a single small-integer near commensurability of orbital period, the construction of a complete formal solution of the equations for the mutual perturbations in a planetary or satellite system, entirely in periodic terms, can be carried out after the use of a transformation of the variables which brings the quadratic terms of the Hamiltonian to a suitable normal form. A method for finding such a transformation is described. 相似文献
18.
R. Scuflaire J. Montalbán S. Théado P.-O. Bourge A. Miglio M. Godart A. Thoul A. Noels 《Astrophysics and Space Science》2008,316(1-4):149-154
The Liège Oscillation code can be used as a stand-alone program or as a library of subroutines that the user calls from a Fortran main program of his own to compute radial and nonradial adiabatic oscillations of stellar models. We describe the variables and the equations used by the program and the methods used to solve them. A brief account is given of the use and the output of the program. 相似文献
19.
R. Baptista 《Astronomische Nachrichten》2004,325(3):181-184
The accretion disc eclipse mapping method is an astrotomographic inversion technique that makes use of the information contained in eclipse light curves to probe the structure, the spectrum and the time evolution of accretion discs in cataclysmic variables. This paper presents examples of eclipse mapping results that have been key to improve our understanding of accretion physics. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
20.
J. Roels 《Celestial Mechanics and Dynamical Astronomy》1975,12(3):327-336
The planar restricted 3-body problem, linearized in the neighborhood of Lagrangian equilibriaL 4 andL 5, has in general two distinct eigenvalues and their opposites. When they are pure imaginary and not multiples of each other, they generate two families of periodic solutions called long and short periodic families. This is essentially a consequence of the famous theorem of Liapunov (Siegel, 1956). We showed (Roels, 1971b) how to solve the problem when the eigenvalues are multiples of each other in building series with negative exponents instead of the integer expansions of Siegel (Roels and Lauterman, 1970). When the eigenvalues are equal, which is the case for the mass ratio of Routh, the problem was solved by Deprit and Henrard (1968) using formal series in ordinary unnormalized variables. That leads to very complicated series because of the use of variables that are not well adapted to the problem. The convergence of the series was proven by Meyer and Schmidt (1971). In this paper we solve the problem by using normalized variables. This brings us to build expansions with fractional exponents. So in summary, normalized variables generate integer series in the non-resonant cases, series with negative exponents in the case of resonancek≥3, and series with fractional exponents when the resonance is 1. 相似文献