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1.
Victor A. Avdyushev 《Celestial Mechanics and Dynamical Astronomy》2003,87(4):383-409
Mainly, the author focuses on Baumgarte's method and its applications in satellite, asteroid, stellar and planetary problems. In the paper arguments are given for the use of energy relations for stabilization in the elliptical two-body problem. Stabilizing properties of Baumgarte's equations and others are discussed. A simple approach is proposed for stabilizing the equations of almost circular motion. By using Baumgarte's technique, the author derives stabilized equations of perturbed restricted three-body problem. It is shown experimentally that stabilization in the problems mentioned above can raise the accuracy of numerical integration by several orders. 相似文献
2.
V. A. Avdyushev 《Solar System Research》2009,43(6):543-551
A Monte Carlo-type method for simulating virtual values of the parameters in inverse orbital dynamics problems for highly
nonlinear cases is proposed. The method is based on imitating Fisher’s statistics employed to specify the confidence region,
and is implemented by solving repeatedly nonlinear least-squares problems with various samples of simulated observations obtainable
by suitable random variations. 相似文献
3.
Some problems in determining the orbits of inner satellites associated with the complex behavior of the target function, which is strongly ravine and which possesses multiple minima in the case of the satellite orbit is determined based on fragmentary observations distributed over a rather long time interval, are studied. These peculiarities of the inverse problems are considered by the example of the dynamics of the inner Jupiter satellites: Amalthea, Thebe, Adrastea, and Metis. Numerical models of the satellite motions whose parameters were determined based on ground-based observations available at the moment to date have been constructed. A composite approach has been proposed for the effective search for minima of the target function. The approach allows one to obtain the respective evaluations of the orbital parameters only for several tens of iterations even in the case of very rough initial approximations. If two groups of observations are available (Adrastea), a formal minimization of the target function is shown to give a solution set, which is the best solution from the point of view of representation of the orbital motion, which is impossible to choose. Other estimates are given characterizing the specific nature of the inverse problems. 相似文献
4.
Victor A. Avdyushev 《Celestial Mechanics and Dynamical Astronomy》2017,129(4):537-552
Orbit determination from a small sample of observations over a very short observed orbital arc is a strongly nonlinear inverse problem. In such problems an evaluation of orbital uncertainty due to random observation errors is greatly complicated, since linear estimations conventionally used are no longer acceptable for describing the uncertainty even as a rough approximation. Nevertheless, if an inverse problem is weakly intrinsically nonlinear, then one can resort to the so-called method of disturbed observations (aka observational Monte Carlo). Previously, we showed that the weaker the intrinsic nonlinearity, the more efficient the method, i.e. the more accurate it enables one to simulate stochastically the orbital uncertainty, while it is strictly exact only when the problem is intrinsically linear. However, as we ascertained experimentally, its efficiency was found to be higher than that of other stochastic methods widely applied in practice. In the present paper we investigate the intrinsic nonlinearity in complicated inverse problems of Celestial Mechanics when orbits are determined from little informative samples of observations, which typically occurs for recently discovered asteroids. To inquire into the question, we introduce an index of intrinsic nonlinearity. In asteroid problems it evinces that the intrinsic nonlinearity can be strong enough to affect appreciably probabilistic estimates, especially at the very short observed orbital arcs that the asteroids travel on for about a hundredth of their orbital periods and less. As it is known from regression analysis, the source of intrinsic nonlinearity is the nonflatness of the estimation subspace specified by a dynamical model in the observation space. Our numerical results indicate that when determining asteroid orbits it is actually very slight. However, in the parametric space the effect of intrinsic nonlinearity is exaggerated mainly by the ill-conditioning of the inverse problem. Even so, as for the method of disturbed observations, we conclude that it practically should be still entirely acceptable to adequately describe the orbital uncertainty since, from a geometrical point of view, the efficiency of the method directly depends only on the nonflatness of the estimation subspace and it gets higher as the nonflatness decreases. 相似文献
5.
Tatyana Bordovitsyna Victor Avdyushev Alexand r Chernitsov 《Celestial Mechanics and Dynamical Astronomy》2001,80(3-4):227-247
A brief survey of the results obtained by the authors in the development and investigation of the algorithms of numerical simulation of the motion of solar system small bodies is given. New approaches to the construction of the algorithms of high-accuracy numerical simulation of the dynamics of small bodies and the methods of the determination of the domain of their possible motions are presented. 相似文献
6.
We propose a numerical method for quick evaluation of the probability that an asteroid will collide with a planet. The method is based on linear mappings of an expected moment of a close approach of the asteroid to the planet and the detection of collisions of the virtual objects with the massive body. The standard way for solving the problem of estimating the collision probability consists in simulating the evolution of the uncertainty cloud numerically based on the stepwise integration of virtual orbits. This is naturally associated with huge processor time costs. The proposed method is tested using the examples of the 2011 AG5 and 2007 VK184 asteroids that are presently in the top of the list of the most dangerous celestial objects. The test results show that linear mappings allow one to obtain the estimates of probabilities quicker by several orders than numerical integration of all virtual orbits. 相似文献
7.
Avdyushev V. A. Bordovitsyna T. V. Baturin A. P. Bakhtigaraev N. S. Levkina P. A. Popandopulo N. A. Saleiko K. V. Tomilova I. V. Chuvashov I. N. 《Solar System Research》2022,56(5):327-337
Solar System Research - The results are presented of a numerical simulation for the motion of a group of geosynchronous objects from positional observations obtained with the unique Zeiss-2000... 相似文献
8.
Victor A. Avdyushev 《Celestial Mechanics and Dynamical Astronomy》2011,110(4):369-388
Determination of orbital parameters from observations is formally a nonlinear inverse problem for solving which evidently
nonlinear methods are required. Meanwhile, an accompanying stage in solving the inverse problem is the evaluation of parametric
accuracy to which, however, linear methods are conventionally applied. This is quite justified if parametric errors caused
by observation errors are rather small, otherwise this is not at all since the nonlinearity of the inverse problem can be
considerable to influence on the evaluations of parametric accuracy especially when the observations are very few. With the
advent of quick-operating and multiprocessor computers, recently one tends to employ statistic simulation of virtual parameter
values for investigating uncertainties in orbits determined from observations. In the paper are just discussed the methods
designed specially for nonlinear statistic simulation of virtual parameter values. Their efficiency is investigated in application
to estimating uncertainties in the orbit of Jovian satellite S/2003 J04 whose orbital parameters are ill-determined owing
to scanty available observations. Indices of nonlinearity are introduced for making decision in the choice between linear
and nonlinear methods. 相似文献
9.
A differential correction using Lieske's analytical theory was applied for a 100-year time interval, and a new system of initial parameters was obtained for numerical simulation of the motion of Jupiter's Galilean satellites. 相似文献
10.
Solar System Research - This paper presents the results of a study of total and intrinsic nonlinearities in inverse problems of the dynamics of Jupiter’s Outer Satellites, observed on very... 相似文献