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1.
C. Beaugé 《Celestial Mechanics and Dynamical Astronomy》1996,64(4):313-350
Starting with a simple Taylor-based expansion of the inverse of the distance between two bodies, we are able to obtain a series expansion of the disturbing function of the three-body problem (planar elliptic case) which is valid for all points of the phase space outside the immediate vicinity of the collision points. In particular, the expansion is valid for very high values of the eccentricity of the perturbed body. Furthermore, in the case of an interior mean-motion resonant configuration, the above-mentioned expression is easily averaged with respect to the synodic period, yielding once again a global expansion of (R) valid for very high eccentricities.Comparisons between these results and the numerically computed exact function are presented for various resonances and values of the eccentricity. Maximum errors are determined in each case and their origin is established. Lastly, we discuss the applicability of the present expansion to practical problems. 相似文献
2.
We consider the particular solutions of the evolutionary system of equations in elements that correspond to planar and spatial circular orbits of the singly averaged Hill problem. We analyze the stability of planar and spatial circular orbits to inclination and eccentricity, respectively. We construct the instability regions of both particular solutions in the plane of parameters of the problem. 相似文献
3.
对边界层理论新结果中出现的一类奇异积分方程w(t)=∫1 t(1-s)(λ+λs+s)/w(s)ds+(1-t)∫t 0s/w(s)ds,t∈(0,1)进行讨论,并得出了上述方程在λ∈(-1/2,0)上正解存在性的新结果。 相似文献
4.
The concept of closest approach is analyzed in Hill’s problem, resulting in a partitioning of the position space. The different
behavior between the direct and retrograde motion is explained analytically, resulting in a simple estimate of the variation
of Hill’s periodic and quasi-circular orbits as a function of the Jacobi constant. The local behavior of the orbits on the
zero velocity surfaces and an analytical definition of local escape and capture in Hill’s problem are also given. 相似文献
5.
For monoparametric familiesf(x,y)=c of planar orbits, created by a planar potentialV(x,y), we introduce the notion of the family boundary curves (FBC). All members of the familyf(x,y)=c are traced in an allowable region of thexy plane, defined by the corresponding FBC, with total energyE=E(c) varying along the family. Family boundary curves are also found for two-parametric familiesf(x,y,b)=c. The relation of equilibrium points and asymptotic orbits, possibly possessed by the potentialV(x,y), to be FBC is studied. 相似文献
6.
Abdul Ahmad 《Celestial Mechanics and Dynamical Astronomy》1995,61(2):181-196
The periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions are well known (Kurcheeva, 1973). Here the stability of these solutions are examined by applying Poncaré's characteristic equation for periodic solutions. It is found that the isoperiodic solutions are stable and all other solutions are unstable. 相似文献
7.
Robe's restricted three-body problem is reanalyzed with a view to incorporate a new assumption, namely that the configuration of the fluid body is that described by an hydrostatic equilibrium figure (Roche's ellipsoid). In the concomitant gravitational field a full treatment of the buoyancy force is given. The pertinent equations of motion are derived, the linear stability of the equilibrium solution is studied and the connection between the effect of the buoyancy forces and a perturbation of the Coriolis force is pointed out. 相似文献
8.
在修改的Ohta_Okamoto数字签名方案基础上,设计出了一个新的(t,n)门限签名方案。该方案具有可验证性和防止内部成员合谋攻击;而且验证者在验证群签名的有效性计算的复杂性与一般个人签名方案一样。该方案的安全性是基于大整数的因式分解,因此在计算上是安全的。 相似文献
9.
吴泽忠 《成都信息工程学院学报》2004,19(2):258-262
在序线性拓扑空间里研究了含有集约束向量极值问题的最优性条件,并建立了充分性和必要性条件. 相似文献
10.
Combining the results of the inverse problem of dynamics with the theory of multiseparability of planar potentials, we find biparametric families of orbits, whose existence guarantees the multiseparability of the potential. We also study the allowed regions of the plane, where these orbits are traced. 相似文献