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221.
通过对测量数字化研究与论证工作,实现矿山测量数字化,有助于提高矿山测量工作的准确性,避免工作失误的发生。针对矿山测量中存在的典型问题,结合自己的工作实践,提出了几点提高矿山测量工作效率的对策。 相似文献
222.
The conditional nonlinear optimal perturbation (CNOP), which is a nonlinear generalization
of the linear singular vector (LSV), is applied in important problems of atmospheric and oceanic
sciences, including ENSO predictability, targeted observations, and ensemble forecast. In this study,
we investigate the computational cost of obtaining the CNOP by several methods. Differences and
similarities, in terms of the computational error and cost in obtaining the CNOP, are compared among
the sequential quadratic programming (SQP) algorithm, the limited memory Broyden-Fletcher-Goldfarb-Shanno
(L-BFGS) algorithm, and the spectral projected gradients (SPG2) algorithm. A theoretical grassland
ecosystem model and the classical Lorenz model are used as examples.
Numerical results demonstrate that the computational error is acceptable with all three algorithms.
The computational cost to obtain the CNOP is reduced by using the SQP algorithm. The experimental
results also reveal that the L-BFGS algorithm is the most effective algorithm among the three
optimization algorithms for obtaining the CNOP. The numerical results suggest a new approach and
algorithm for obtaining the CNOP for a large-scale optimization problem. 相似文献
223.
We present a numerical study of the set of orbits of the planar circular restricted three body problem which undergo consecutive
close encounters with the small primary, or orbits of second species. The value of the Jacobi constant is fixed, and we restrict
the study to consecutive close encounters which occur within a maximal time interval. With these restrictions, the full set
of orbits of second species is found numerically from the intersections of the stable and unstable manifolds of the collision
singularity on the surface of section that corresponds to passage through the pericentre. A ‘skeleton’ of this set of curves
can be computed from the solutions of the two-body problem. The set of intersection points found in this limit corresponds
to the S-arcs and T-arcs of Hénon’s classification which verify the energy and time constraints, and can be used to construct
an alphabet to describe the orbits of second species. We give numerical evidence for the existence of a shift on this alphabet
that describes all the orbits with infinitely many close encounters with the small primary, and sketch a proof of the symbolic
dynamics. In particular, we find periodic orbits that combine S-type and T-type quasi-homoclinic arcs. 相似文献
224.
G. A. Tsirogiannis E. A. Perdios V. V. Markellos 《Celestial Mechanics and Dynamical Astronomy》2009,103(1):49-78
We present an improved grid search method for the global computation of periodic orbits in model problems of Dynamics, and
the classification of these orbits into families. The method concerns symmetric periodic orbits in problems of two degrees
of freedom with a conserved quantity, and is applied here to problems of Celestial Mechanics. It consists of two main phases;
a global sampling technique in a two-dimensional space of initial conditions and a data processing procedure for the classification
(clustering) of the periodic orbits into families characterized by continuous evolution of the orbital parameters of member
orbits. The method is tested by using it to recompute known results. It is then applied with advantage to the determination
of the branch families of the family f of retrograde satellites in Hill’s Lunar problem, and to the determination of irregular families of periodic orbits in a
perturbed Hill problem, a species of families which are difficult to find by continuation methods.
相似文献
225.
New doubly-symmetric families of comet-like periodic orbits in the spatial restricted (N + 1)-body problem 总被引:1,自引:0,他引:1
For any positive integer N ≥ 2 we prove the existence of a new family of periodic solutions for the spatial restricted (N +1)-body problem. In these solutions the infinitesimal particle is very far from the primaries. They have large inclinations
and some symmetries. In fact we extend results of Howison and Meyer (J. Diff. Equ. 163:174–197, 2000) from N = 2 to any positive integer N ≥ 2.
相似文献
226.
We consider periodic halo orbits about artificial equilibrium points (AEP) near to the Lagrange points L
1 and L
2 in the circular restricted three body problem, where the third body is a low-thrust propulsion spacecraft in the Sun–Earth
system. Although such halo orbits about artificial equilibrium points can be generated using a solar sail, there are points
inside L
1 and beyond L
2 where a solar sail cannot be placed, so low-thrust, such as solar electric propulsion, is the only option to generate artificial
halo orbits around points inaccessible to a solar sail. Analytical and numerical halo orbits for such low-thrust propulsion
systems are obtained by using the Lindstedt Poincaré and differential corrector method respectively. Both the period and minimum
amplitude of halo orbits about artificial equilibrium points inside L
1 decreases with an increase in low-thrust acceleration. The halo orbits about artificial equilibrium points beyond L
2 in contrast show an increase in period with an increase in low-thrust acceleration. However, the minimum amplitude first
increases and then decreases after the thrust acceleration exceeds 0.415 mm/s2. Using a continuation method, we also find stable artificial halo orbits which can be sustained for long integration times
and require a reasonably small low-thrust acceleration 0.0593 mm/s2. 相似文献
227.
Giovanni Federico Gronchi 《Celestial Mechanics and Dynamical Astronomy》2009,103(4):301-326
Charlier’s theory (1910) provides a geometric interpretation of the occurrence of multiple solutions in Laplace’s method of
preliminary orbit determination, assuming geocentric observations. We introduce a generalization of this theory allowing to
take into account topocentric observations, that is observations made from the surface of the rotating Earth. The generalized
theory works for both Laplace’s and Gauss’ methods. We also provide a geometric definition of a curve that generalizes Charlier’s
limiting curve, separating regions with a different number of solutions. The results are generically different from Charlier’s:
they may change according to the value of a parameter that depends on the observations. 相似文献
228.
When μ is smaller than Routh’s critical value μ
1 = 0.03852 . . . , two planar Lyapunov families around triangular libration points exist, with the names of long and short
period families. There are periodic families which we call bridges connecting these two Lyapunov families. With μ increasing from 0 to 1, how these bridges evolve was studied. The interval (0,1) was divided into six subintervals (0, μ
5), (μ
5, μ
4), (μ
4, μ
3), (μ
3, μ
2), (μ
2, μ
1), (μ
1, 1), and in each subinterval the families B(pL, qS) were studied, along with the families B(qS, qS′). Especially in the interval (μ
2, μ
1), the conclusion that the bridges B(qS, qS′) do not exist was obtained. Connections between the short period family and the bridges B(kS, (k + 1)S) were also studied. With these studies, the structure of the web of periodic families around triangular libration points
was enriched. 相似文献
229.
A. Dermanis 《Journal of Geodesy》1998,72(2):71-100
Motivated by the existing theory of the geometric characteristics of linear generalized inverses of linear mappings, an attempt
is made to establish a corresponding mathematical theory for nonlinear generalized inverses of nonlinear mappings in finite-
dimensional spaces. The theory relies on the concept of fiberings consisting of disjoint manifolds (fibers) in which the domain
and range spaces of the mappings are partitioned. Fiberings replace the quotient spaces generated by some characteristic subspaces
in the linear case. In addition to the simple generalized inverse, the minimum-distance and the x
0-nearest generalized inverse are introduced and characterized, in analogy with the least-squares and the minimum-norm generalized
inverses of the linear case. The theory is specialized to the geodetic mapping from network coordinates to observables and
the nonlinear transformations (Baarda's S-transformations) between different solutions are defined with the help of transformation parameters obtained from the solution
of nonlinear equations. In particular, the transformations from any solution to an x
0-nearest solution (corresponding to Meissl's inner solution) are given for two- and three-dimensional networks for both the
similarity and the rigid transformation case. Finally the nonlinear theory is specialized to the linear case with the help
of the singular-value decomposition and algebraic expressions with specific geometric meaning are given for all possible types
of generalized inverses.
Received: 11 April 1996 / Accepted: 19 April 1997 相似文献
230.
In this paper we present Runge-Kutta-Nyström (RKN) pairs of orders 4(3) and 6(4). We choose a test orbit from the Kepler problem to integrate for a specific tolerance. Then we train the free parameters of the above RKN4(3) and RKN6(4) families to perform optimally. For that we form a neural network approach and minimize its objective function using a differential evolution optimization technique. Finally we observe that the produced pairs outperform standard pairs from the literature for Pleiades orbits and Kepler problem over a wide range of eccentricities and tolerances. 相似文献