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1.
This paper describes a practical method for finding the invariant orbits in J
2 relative dynamics. Working with the Hamiltonian model of the relative motion including the J
2 perturbation, the effective differential correction algorithm for finding periodic orbits in three-body problem is extended
to formation flying of Earth’s orbiters. Rather than using orbital elements, the analysis is done directly in physical space,
which makes a direct connection with physical requirements. The asymptotic behavior of the invariant orbit is indicated by
its stable and unstable manifolds. The period of the relative orbits is proved numerically to be slightly different from the
ascending node period of the leader satellite, and a preliminary explanation for this phenomenon is presented. Then the compatibility
between J
2 invariant orbit and desired relative geometry is considered, and the design procedure for the initial values of the compatible
configuration is proposed. The influences of measure errors on the invariant orbit are also investigated by the Monte–Carlo
simulation.
The project supported by the Innovation Foundation of Beihang University for Ph.D. Graduates, and the National Natural Science
Foundation of China (60535010). 相似文献
2.
Ding Xie-ping 《应用数学和力学(英文版)》2003,24(6):659-672
A new family of set-valued mappings from a topological space into generalized convex spaces was introduced and studied. By
using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements
for the family of set-valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems
improve, unify and generalize many important results in recent literature.
Contributed by DING Xie-ping
Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan
Province of China ([2000]25)
Biography: DING Xie-ping (1938∼) 相似文献
3.
Ding Xie-ping 《应用数学和力学(英文版)》2003,24(9):1017-1024
By applying existence theorems of maximal elements for a family of GB-majorized mappings in a product space of G-convex spaces, some coincidence theorem, Fan-Browder type fixed point theorem
and some existence theorems of solutions for a system of minimax inequalities are proved under noncompact setting of G-convex
spaces. These theorems improve and generalize many important known results in literature.
Contributed by Duping Xie-ping
Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan
Province ([2000]25)
Biography: Duping Xie-ping (1938∼), Professor (E-mail: dingxip@sichu.edu.cn) 相似文献
4.
丁协平 《应用数学和力学(英文版)》2007,28(12):1569-1579
This paper is a continuum of the preceding paper of author. Some new systems of generalized vector quasi-equilibrium problems
involving condensing mappings are introduced and studied in locally FC-uniform spaces. By applying the existence theorem of maximal elements of condensing set-valued mappings in locally FC-uniform spaces obtained by author in the preceding paper, some new existence theorems of solutions for the systems of generalized
vector quasi-equilibrium problems are proved in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces.
Project supported by the Natural Science Foundation of Sichuan Education Department of China (No. 2003A081 and SZD0406) 相似文献
5.
When using H∞ techniques to design decentralized controllers for large systems,the whole system is divided into subsystems, which are analysed using H∞ control theorybefore being recombined. An analogy was established with substructural analysis instructural mechanics, in which H∞ decentralized control theory corresponds to substructuralmodal synthesis theory so that the optimal H∞ norm of the whole system corresponds to thefundamental vibration frequency of the whole structure. Hence, modal synthesismethodology and the extended Wittrick-Williams algorithm were transplanted from structuralmechanics to compute the optimal H∞ norm of the control system. The orthogonality and theexpansion theorem of eigenfunctions of the subsystems H∞ control are presented in part(I) of the paper. The modal synthesis method for computation of the optimal H∞ norm ofdecentralized control systems and numerical examples are presented in part (Ⅱ). 相似文献
6.
TheT
ε
*
integral was calculated on the surface of single edge notched, three-point bend (SE(B)) specimens using experimentally obtained
displacements. Comparison was made withT
ε
*
calculated with the measured surface displacements andT
ε
*
calculated at several points through the thickness of a finite element (FE) model of the SE(B) specimen. Good comparison
was found between the surfaceT
ε
*
calculated from displacements extracted from the FE model and the surfaceT
ε
*
calculated from experimentally obtained displacements. The computedT
ε
*
integral was also observed to decrease as the crack front was traversed from the surface to the mid-plane of the specimen.
Mid-planeT
ε
*
values tend to be approximately 10% of the surface values. 相似文献
7.
When using H∞ techniques to design decentralized controllers for large systems, the whole system is divided into subsystems, which are analysed using H∞ control theorybefore being recombined. An analogy was established with substructural analysis instructural mechanics, in which H∞ decentralized control theory corresponds to substructuralmodal synthesis theory so that the optimal H∞ norm of the whole system corresponds to thefundamental vibration frequency of the whole structure. Hence, modal synthesismethodology and the extended Wittrick-Williams algorithm were transplanted from structuralmechanics to compute the optimal H∞ norm of the control system. The orthogonality and theexpansion theorem of eigenfunctions of the subsystems H~ control are presented in part (I)of the paper. The modal synthesis method for computation of the optimal H∞ norm ofdecentralized control systems and numerical examples are presented in part (Ⅱ). 相似文献
8.
A new class of g-η-monotone mappings and a class of generalized implicit variational-like inclusions involving g-η-monotone mappings are introduced. The resolvent operator of g-η-monotone mappings is defined and its Lipschitz continuity is presented. An iterative algorithm for approximating the solutions of generalized implicit variational-like inclusions is suggested and analyzed. The convergence of iterative sequences generated by the algorithm is also proved. 相似文献
9.
Periodic solution of m order linear neutral equations with constant coefficient and time delays was studied. Existence and
uniqueness of 2 T-periodic solutions for the equation were discussed by using the method of Fourier series. Some new necessary
and sufficient conditions of existence and uniqueness of 2T-periodic solutions for the equation are obtained. The main result
is used widely. It contains results in some correlation paper for its special case, improves and extends the main results
in them. Existence of periodic solution for the equation in larger number of particular case can be checked by using the result,
but cannot be checked in another paper. In other words, the main result in this paper is most generalized for (1), the better
result cannot be found by using the same method.
Foundation item: the Natural Science Foundation of Yunnan Education Committee (990002)
Biography: ZHANG Bao-sheng (1962-) 相似文献
10.
Ding Xie-ping 《应用数学和力学(英文版)》2003,24(5):499-508
A new class of constrained multiobjective games with infinite players in noncompact locally convex H-spaces without linear
structure are introduced and studied. By applying a Fan-Glicksberg type fixed point theorem for upper semicontinuous set-valued
mappings with closed acyclic values and a maximum theorem, several existence theorems of weighted Nath-equilibria and Pareto
equilibria for the constrained multiobjective games are proved in noncompact locally convex H-spaces. These theorems improve,
unify and generalize the corresponding results of the multiobjective games in recent literatures.
Contributed by Ding Xie-ping
Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan
Province ([2000]25)
Biography: Ding Xie-ping (1938-) 相似文献
11.
Petty's conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty's conjectured projection inequality is developed by using the notions of the Lp-mixed volume and the Lp-dual mixed volume, the relation of the Lp-projection body and the geometric body Г-pK, the Bourgain-Milman inequality and the Lp-Bnsemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body Г-pK, the reverses of Lp-version of the Petty's conjectured projection inequality and the Lp-Petty projection inequality are given, respectively. 相似文献
12.
Shape-memory TiNi fiber-reinforced/epoxy matrix composites have been fabricated, and the suppression of crack-tip stress intensity
and the change in fracture toughness have been systematically investigated. Stress-strain data for these composite specimens
with notches at various angles and different crack lengths in the transverse direction have been measured in tensile tests.
The stress intensity factor at the crack tip is experimentally determined from photoelastic fringe patterns. The decreases
inK values are attributed to the compressive stress field in the matrix induced when the pre-strains of the TiNi fiber contract
to their initial length upon heating above the austenitic final temperature. We present the influences of the pre-strain of
TiNi fibers and the compressive domain size between a crack tip and fiber on theK value. 相似文献
13.
Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Gre... 相似文献
14.
The new coupled MKdV hierarchy is obtained. By using gauge transformation, the constrained flow, the integrable system and
Lax representation for the coupled MKdV hierarchy were first constructed from the AKNS hierarchy and then using the Lax representation,
the r-matrix for the constrained flow of the coupled MKdV hierarchy was constructed. The second set of conserved integrals
of this constrained flow and their involutivity were also given.
Biography: LIU Xiang-lin (1966-), Associate Professor (E-mail: zhangbc@sjzri.edu.cn) 相似文献
15.
Novid Beheshti Alexey A. Burluka Michael Fairweather 《Theoretical and Computational Fluid Dynamics》2007,21(5):381-397
In a series of recent works, R. Borghi and co-workers proposed a new Eulerian model of two-phase turbulent flows which introduced
a transport equation for the average area of the liquid–gas interface. This work is devoted to the assessment of this model’s
ability to predict the effects of liquid properties and injection regimes on the atomisation quality. Air-assisted atomisation,
for which extensive experimental data are available, is chosen as a test case. It is shown that the model predictions are
in good agreement with the observed trends for a wide range of variations of the liquid properties, such as density and surface
tension, as well as the injection regimes, defined by the liquid and gas jet exit velocities.
相似文献
16.
王广民 《应用数学和力学(英文版)》2007,28(12):1561-1568
First, the notions of the measure of noncompactness and condensing set-valued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of set-valued mappings
involving condensing mappings is proved in locally FC-uniform spaces. As applications, some new equilibrium existence theorems of generalized game involving condensing mappings
are established in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Some further applications of our results to the systems of generalized vector quasi-equilibrium problems
will be given in a follow-up paper.
Project supported by the Natural Science Foundation of Sichuan Education Department of China (Nos. 2003A081 and SZD0406) 相似文献
17.
One of the most promising approaches to characterizing the stable tearing process for lower constraint configurations in metallic
materials has been indicated to be the crack tip opening angle (CTOA) criterion. In this paper we examine the effect of measurement
distance selection and the impact of measurement procedures/analysis on the experimental CTOA-Δa resistance curve behavior of a Ti-6Al-4V and an Al5083 alloy. A new, systematic procedure for carrying out the experimental,
surface CTOA measurement process has been used, which has uncovered artifacts of measurement distance selection that have
not been presented prior to this study. By studying the CTOA-Δa behavior using a rigidly defined and consistent method, it is apparent that the measurement distance behind the crack tip
at which angles are measured has a direct impact on the shape of the early transitional behavior of the CTOA-Δa behavior as well as the critical, experimental CTOA values produced. 相似文献
18.
The weakened Hilberts 16th problem for symmetric planar perturbed polynomial Hamiltonian systems is considered. An example of Z8-equivariant planar perturbed Hamiltonian systems is constructed. By using bifurcation theory of planar dynamical systems and the method of detection functions, under the help of numerical analysis, it is shown that there exist parameter groups such that this perturbed Hamiltonian polynomial vector field of degree 7 has at least72=49 limit cycles with Z8 symmetry. It also gives rise to different configurations of limit cycles forming compound eyes.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th
birthday. 相似文献
19.
The paper first proves a characteristic property in FC-spaces. By the use of the connectedness of sets, a parametric type of KKM theorem is then established in noncompact FC-spaces by introducing a linear ordered space. As a consequence, some recent results, such as noncompact minimax inequalities, saddle point theorem, and section theorem, are improved. The results generalize the corresponding results in the literatures. 相似文献
20.
A class of nonlinear boundary value problems (BVP) for the second-order E2 class elliptic systems in general form is discussed. By introducing a kind of transformation, this kind of BVP is reduced
to a class of generalized nonlinear Riemann-Hilbert BVP. And then some singular integral operators are introduced to establish
the equivalent nonlinear singular integral equations. The solvability is proved under some suitable hypotheses by means of
the properties of singular integral operators and the function theoretic methods.
Foundation items: the National Natural Science Foundation of China (19671056); Shanghai Municipal Natural Scientific Foundation (99ZA14030,
01ZA14023); Jiangxi Provincial Natural Scientific Foundation (981102, 0211014)
Biographies: LI Ming-zhong (1935−); XU Ding-hua (1967−) 相似文献