共查询到20条相似文献，搜索用时 62 毫秒
1.
Jörg Waldvogel 《Celestial Mechanics and Dynamical Astronomy》2008,102(1-3):149-162
Quaternions have been found to be the ideal tool for describing and developing the theory of spatial regularization in Celestial Mechanics. This article corroborates the above statement. Beginning with a summary of quaternion algebra, we will describe the regularization procedure and its consequences in an elegant way. Also, an alternative derivation of the theory of Kepler motion based on regularization will be given. Furthermore, we will consider the regularization of the spatial restricted three-body problem, i.e. the spatial generalization of the Birkhoff transformation. Finally, the perturbed Kepler motion will be described in terms of regularized variables. 相似文献
2.
J. Baumgarte 《Celestial Mechanics and Dynamical Astronomy》1972,5(4):490-501
A stabilization of the classical equations of two-body motion is offered. It is characterized by the use of the regularizing independent variable (eccentric anomaly) and by the addition of a control-term to the differential equations. This method is related to the KS-theory (Stiefel, 1970) which performed for the first time a stabilization of the Kepler motion. But in contrast to the KS-theory our method does not transform the coordinates of the particle. As far as the theory of stability and the numerical experiments are concerned we restrict ourselves to thepure Kepler motion. But, of course, the stabilizing devices will also improve the accuracy of the computation of perturbed orbits. We list, therefore, also the equations of the perturbed motion. 相似文献
3.
Mervat El-Sayed Awad 《Earth, Moon, and Planets》1988,43(1):7-20
In this paper of the series, a special perturbation technique of Encke-type associated with the KS regularized variables will be developed for satellite motions in the Earth's gravitational field with axial symmetry. Its computational algorithm is of recursive nature and could be applied for any perturbed conic motion whatever the number of the zonal harmonic coefficients may be. Applications of the algorithm are also included.Now at the Department of Mathematics, Girls College of Education, Jeddah, Saudi Arabia. 相似文献
4.
V. A. Shefer 《Celestial Mechanics and Dynamical Astronomy》1990,49(2):197-207
A review is presented of the author's results on application of regularizing and stabilizing KS- transformation in the problem of investigation of the motion of unusual minor planets and comets. Two models of the motion of a minor body are considered, viz. the perturbed two body problem and the perturbed restricted three body problem. The variational equations in KS-variables and transformations for obtaining the matrix of partial derivatives of the instantaneous physical parameters of motion with respect to their initial values are presented. The peculiarities of the implementation of the algorithms developed as programs on a computer are described. The original results of the investigation of the efficiency of the developed algorithms and programs are discussed using as an example the motion of unusual minor planets Icarus and Geographos as well as comets Halley, Honda-Mrkos-Pajdusakova and Gehrels 3. 相似文献
5.
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
6.
P. Exertier 《Celestial Mechanics and Dynamical Astronomy》1993,57(1-2):137-153
The monitoring of the perturbed motion of artificial satellites since the 1960's has provided a valuable resource for improved activities in geodesy. These observations and the improved geodetic techniques they fostered have provided an unparalleled means for studying both the gravity field and the Earth's shape. In this paper, we will review the various determinations of the Earth's gravity field produced at many research centers over the years from space techniques. The specific methods which have been used to measure our planet, such as satellite altimetry and satellite orbital perturbation analyses (over short and long periods of time), will be compared. 相似文献
7.
论述的短弧定轨,是指在无先验信息情况下又避开多变元迭代的初轨计算方法,它需要相应的动力学问题有一能反映短弧内达到一定精度的近似分析解．探测器进入月球引力作用范围后接近月球时可以处理成相对月球的受摄二体问题,而在地球附近,则可处理成相对地球的受摄二体问题,但在整个过渡段的力模型只能处理成一个受摄的限制性三体问题．而限制性三体问题无分析解,即使在月球引力作用范围外,对于大推力脉冲式的过渡方式,相对地球的变化椭圆轨道的偏心率很大(超过Laplace极限),在考虑月球引力摄动时亦无法构造摄动分析解．就此问题,考虑在地球非球形引力(只包含J2项)和月球引力共同作用下,构造了探测器飞抵月球过渡轨道段的时间幂级数解,在此基础上给出一种受摄二体问题意义下的初轨计算方法,经数值验证,定轨方法有效,可供地面测控系统参考． 相似文献
8.
E.D. Kuznetsov 《Planetary and Space Science》1997,45(12):1595-1606
The equation for calculation of the required accuracy of the perturbing bodies motion theories is obtained. The equation relates the accuracy required to take into account perturbing acceleration, acting on the perturbed body, with the accuracy of the motion theory of the perturbing body. The solutions for estimation of the required accuracy both for the inner and the external cases in the spherical coordinates are coincided. The solution for the calculation of the required accuracy for the general case (combining the inner and the external cases) in Cartesian coordinates is obtained. The special cases for the solution in Cartesian coordinates are studied. As an example, the estimations of the required accuracy of the motion theories of the solar system planets for some perturbed bodies (the near-Earth asteroid 4179 Toutatis, the main belt asteroid 208 Larcimosa, the trojan asteroid 588 Achilles, the centaur asteroid 5145 Pholus, the Kuiper belt asteroid 1995 QZ9, the comet Halley) are obtained. The conditions of the use of the obtained results are discussed. 相似文献
9.
Zachary E. Wardell 《Monthly notices of the Royal Astronomical Society》2002,334(1):149-155
A model of three-body motion is developed which includes the effects of gravitational radiation reaction. The radiation reaction due to the emission of gravitational waves is the only post-Newtonian effect that is included here. For simplicity, all of the motion is taken to be planar. Two of the masses are viewed as a binary system, and the third mass, whose motion will be a fixed orbit around the centre-of-mass of the binary system, is viewed as a perturbation. This model aims to describe the motion of a relativistic binary pulsar that is perturbed by a third mass. Numerical integration of this simplified model reveals that, given the right initial conditions and parameters, one can see resonances. These ( m , n ) resonances are defined by the resonance condition, mω =2 n Ω , where m and n are relatively prime integers, and ω and Ω are the angular frequencies of the binary orbit and third mass orbit (around the centre-of-mass of the binary), respectively. The resonance condition consequently fixes a value for the semimajor axis of the binary orbit for the duration of the resonance; therefore the binary energy remains constant on average, while its angular momentum changes during the resonance. 相似文献
10.
V. A. Brumberg 《Celestial Mechanics and Dynamical Astronomy》1978,18(4):319-336
For treating the perturbed two-body problem in rectangular coordinates a new method is developed. The method is based on the reduction of the variational equations of the two-body problem with arbitrary elements to the Jordan system. The equations of perturbed motion rewritten in the quasi-Jordan form are subjected to a transformation excluding fast variables and leading to a system governing the long term evolution of motion. The method may be easily extended to the problem of the heliocentric motion of the major planets. For performing this method on computer it is suitable to use facilities of Poissonian and Keplerian processors. 相似文献
11.
V. A. Shefer 《Solar System Research》2003,37(4):326-332
A new method is suggested for finding the preliminary orbit from three complete measurements of the angular coordinates of a celestial body developed by analogy with the classic Lagrange–Gauss method. The proposed method uses the intermediate orbit that we had constructed in an earlier paper based on two position vectors and the corresponding time interval. This intermediate orbit allows for most of the perturbations in the motion of the body. Using the orbital motion of asteroid 1566 Icarus as an example, we compare the results obtained by applying the classic and the new method. The comparison shows the new method to be highly efficient for studying perturbed motion. It is especially efficient if applied to high-precision observational data covering short orbital arcs. 相似文献
12.
S. A. Gasanov 《Astronomy Letters》2007,33(12):827-843
The problem of the motion of a star inside a layered inhomogeneous rotating elliptical galaxy with a variable mass is considered. We have found an analogue of the Jacobi integral and determined the possible regions of motion. A solution to the equations of perturbed motion has been obtained. 相似文献
13.
O. M. Kochetova 《Solar System Research》2004,38(1):66-75
Masses of 19 asteroids have been determined from the analysis of their gravitational effect on the motion of perturbed bodies. The following asteroids were selected as perturbed bodies: (1) those which had single close encounters with the perturbing asteroid; (2) those whose mean motion was in a 1 : 1 commensurability with that of the perturber and which had close or moderate recurrent encounters with the perturber. The perturber mass was determined from observations of several tens of perturbed asteroids that were selected from these two groups. The selection criterion was the error of the mass determined from observations of only one asteroid. Positional observations of the asteroids on the interval 1900–2002 were used. The masses were determined with errors by an order-half an order of magnitude smaller than the masses found. The results are compared with those of other authors. 相似文献
14.
V. A. Shefer 《Celestial Mechanics and Dynamical Astronomy》2002,82(1):19-59
A method of construction of intermediate orbits for approximating the real motion of celestial bodies in the initial part of trajectory is proposed. The method is based on introducing a fictitious attracting centre with a time-variable gravitational parameter. The variation of thisparameter is assumed to obey the Eddington–Jeans mass-variationlaw. New classes of orbits having first-, second-, and third-order tangency to the perturbed trajectory at the initial instant of time are constructed. For planar motion, the tangency increases by one or two orders. The constructed intermediate orbits approximate the perturbed motion better than the osculating Keplerian orbit and analogous orbits of otherauthors. The applications of the orbits constructed in Encke's methodfor special perturbations and in the procedure for predicting themotion in which the perturbed trajectory is represented by a sequenceof short arcs of the intermediate orbits are suggested.The use of the constructed orbits is especially advantageous in the investigation of motion under the action of large perturbations. 相似文献
15.
B. Zafiropoulos 《Astrophysics and Space Science》1987,137(1):139-149
The aim of this investigation is to present the periodic and secular perturbations of the orbital elements of close binary systems due to tidal lag in latitude. The variational equations of the problem of plane motion will be set up in terms of the rectengular componentsR, S, andW of the disturbing accelerations. These equations are highly nonlinear with respect to the orbital elements and we present analytic approximations to the effects produced by the perturbing acceleration due to dynamical tides lagging in latitude. The perturbed elements of the orbit have been expressed by means of Hansen coefficients in the compact form of summations. 相似文献
16.
I. M. Belen'kii 《Celestial Mechanics and Dynamical Astronomy》1981,23(1):9-32
This paper deals with a method of regularization and linearization of the equations of motion in the central force-field, when the potential is given.This method of regularization of the equations of motion is known (Sundman, 1913), and is based on the transformation of time by means of introducing a new independent variable.In this article a condition has been obtained for the regularizing function when the potential is given.Some examples of the perturbed Keplerian motions are discussed. 相似文献
17.
E. Stiefel 《Celestial Mechanics and Dynamical Astronomy》1976,14(1):85-90
For near-parabolic orbits the distinction between coordinates and elements disappears provided the KS-technique is used. In KS-variables a pure parabolic motion is described by linear functions. Advantage is taken of that fact for establishing numerical procedures in perturbed near-parabolic cases. 相似文献
18.
Carolin Früh Thomas M. Kelecy Moriba K. Jah 《Celestial Mechanics and Dynamical Astronomy》2013,117(4):385-404
The orbital and attitude dynamics of uncontrolled Earth orbiting objects are perturbed by a variety of sources. In research, emphasis has been put on operational space vehicles. Operational satellites typically have a relatively compact shape, and hence, a low area-to-mass ratio (AMR), and are in most cases actively or passively attitude stabilized. This enables one to treat the orbit and attitude propagation as decoupled problems, and in many cases the attitude dynamics can be neglected completely. The situation is different for space debris objects, which are in an uncontrolled attitude state. Furthermore, the assumption that a steady-state attitude motion can be averaged over data reduction intervals may no longer be valid. Additionally, a subset of the debris objects have significantly high area-to-mass ratio (HAMR) values, resulting in highly perturbed orbits, e.g. by solar radiation pressure, even if a stable AMR value is assumed. Note, this assumption implies a steady-state attitude such that the average cross-sectional area exposed to the sun is close to constant. Time-varying solar radiation pressure accelerations due to attitude variations will result in un-modeled errors in the state propagation. This work investigates the evolution of the coupled attitude and orbit motion of HAMR objects. Standardized pieces of multilayer insulation (MLI) are simulated in a near geosynchronous orbits. It is assumed that the objects are rigid bodies and are in uncontrolled attitude states. The integrated effects of the Earth gravitational field and solar radiation pressure on the attitude motion are investigated. The light curves that represent the observed brightness variations over time in a specific viewing direction are extracted. A sensor model is utilized to generate light curves with visibility constraints and magnitude uncertainties as observed by a standard ground based telescope. The photometric models will be needed when combining photometric and astrometric observations for estimation of orbit and attitude dynamics of non-resolved space objects. 相似文献
19.
S. A. Gasanov 《Astronomy Letters》2001,27(2):124-133
The plane motion of a mass point inside an inhomogeneous rotating ellipsoidal body with a homothetic density distribution is considered. The force function of the problem is expanded in terms of the ellipsoid's second eccentricities up to the fourth order, which are taken as small parameters. We derive an expression for the perturbing function and solve the equations of perturbed motion in orbital elements. 相似文献
20.
Using alternative independent variables in lieu of time has important advantages when propagating the partial derivatives of the trajectory. This paper focuses on spacecraft relative motion, but the concepts presented here can be extended to any problem involving the variational equations of orbital motion. A usual approach for modeling the relative dynamics is to evaluate how the reference orbit changes when modifying the initial conditions slightly. But when the time is a mere dependent variable, changes in the initial conditions will result in changes in time as well: a time delay between the reference and the neighbor solution will appear. The theory of asynchronous relative motion shows how the time delay can be corrected to recover the physical sense of the solution and, more importantly, how this correction can be used to improve significantly the accuracy of the linear solutions to relative motion found in the literature. As an example, an improved version of the Clohessy-Wiltshire (CW) solution is presented explicitly. The correcting terms are extremely compact, and the solution proves more accurate than the second and even third order CW equations for long propagations. The application to the elliptic case is also discussed. The theory is not restricted to Keplerian orbits, as it holds under any perturbation. To prove this statement, two examples of realistic trajectories are presented: a pair of spacecraft orbiting the Earth and perturbed by a realistic force model; and two probes describing a quasi-periodic orbit in the Jupiter-Europa system subject to third-body perturbations. The numerical examples show that the new theory yields reductions in the propagation error of several orders of magnitude, both in position and velocity, when compared to the linear approach. 相似文献