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71.
L. K. Babadzanjanz 《Celestial Mechanics and Dynamical Astronomy》1993,56(3):427-449
In connection with the publication (Wang Qiu-Dong, 1991) the Poincaré type methods of obtaining the maximal solution of differential equations are discussed. In particular, it is shown that the Wang Qiu-Dong'sglobal solution of the N-body problem has been obtained in Babadzanjanz (1979). First the more general results on differential equations have been published in Babadzanjanz (1978). 相似文献
72.
The accelerated Kepler problem (AKP) is obtained by adding a constant acceleration to the classical two-body Kepler problem.
This setting models the dynamics of a jet-sustaining accretion disk and its content of forming planets as the disk loses linear
momentum through the asymmetric jet-counterjet system it powers. The dynamics of the accelerated Kepler problem is analyzed
using physical as well as parabolic coordinates. The latter naturally separate the problem’s Hamiltonian into two unidimensional
Hamiltonians. In particular, we identify the origin of the secular resonance in the AKP and determine analytically the radius
of stability boundary of initially circular orbits that are of particular interest to the problem of radial migration in binary
systems as well as to the truncation of accretion disks through stellar jet acceleration. 相似文献
73.
Taeyoung Lee Melvin Leok N. Harris McClamroch 《Celestial Mechanics and Dynamical Astronomy》2007,98(2):121-144
Equations of motion, referred to as full body models, are developed to describe the dynamics of rigid bodies acting under
their mutual gravitational potential. Continuous equations of motion and discrete equations of motion are derived using Hamilton’s
principle. These equations are expressed in an inertial frame and in relative coordinates. The discrete equations of motion,
referred to as a Lie group variational integrator, provide a geometrically exact and numerically efficient computational method
for simulating full body dynamics in orbital mechanics; they are symplectic and momentum preserving, and they exhibit good
energy behavior for exponentially long time periods. They are also efficient in only requiring a single evaluation of the
gravity forces and moments per time step. The Lie group variational integrator also preserves the group structure without
the use of local charts, reprojection, or constraints. Computational results are given for the dynamics of two rigid dumbbell
bodies acting under their mutual gravity; these computational results demonstrate the superiority of the Lie group variational
integrator compared with integrators that are not symplectic or do not preserve the Lie group structure. 相似文献
74.
E. A. Perdios 《Celestial Mechanics and Dynamical Astronomy》2007,99(2):85-104
This paper deals with the Sitnikov family of straight-line motions of the circular restricted three-body problem, viewed as
generator of families of three-dimensional periodic orbits. We study the linear stability of the family, determine several
new critical orbits at which families of three dimensional periodic orbits of the same or double period bifurcate and present
an extensive numerical exploration of the bifurcating families. In the case of the same period bifurcations, 44 families are
determined. All these families are computed for equal as well as for nearly equal primaries (μ = 0.5, μ = 0.4995). Some of the bifurcating families are determined for all values of the mass parameter μ for which they exist. Examples of families of three dimensional periodic orbits bifurcating from the Sitnikov family at double
period bifurcations are also given. These are the only families of three-dimensional periodic orbits presented in the paper
which do not terminate with coplanar orbits and some of them contain stable parts. By contrast, all families bifurcating at
single-period bifurcations consist entirely of unstable orbits and terminate with coplanar orbits. 相似文献
75.
The existence and stability of triangular libration points in the relativistic restricted three-body problem has been studied.
It is found that L4,5 are unstable in the whole range 0 ≤ μ ≤ 1/2 in contrast to the classical restricted three-body problem where they are stable
for 0 < μ < μ0, where μ is the mass parameter and μ0 = 0.03852....
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
76.
We study the motion of an infinitesimal mass point under the gravitational action of three mass points of masses μ, 1–2μ and
μ moving under Newton's gravitational law in circular periodic orbits around their center of masses. The three point masses
form at any time a collinear central configuration. The body of mass 1–2μ is located at the center of mass. The paper has
two main goals. First, to prove the existence of four transversal ejection–collision orbits, and second to show the existence
of an uncountable number of invariant punctured tori. Both results are for a given large value of the Jacobi constant and
for an arbitrary value of the mass parameter 0<μ≤1/2.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
77.
78.
结合吉青岭隧道的工程实际,分析了浅埋偏压不良地质条件下隧道进口段的施工风险,提出了采取初期支护加强,短循环开挖,初期支护封闭等综合地质病害预防措施。 相似文献
79.
80.
P. P. Hallan Sanjay Jain K. B. Bhatnagar 《Celestial Mechanics and Dynamical Astronomy》2000,77(3):157-184
The non-linear stability of L
4 in the restricted three-body problem has been studied when the bigger primary is a triaxial rigid body with its equatorial
plane coincident with the plane of motion. It is found that L
4 is stable in the range of linear stability except for three mass ratios:
where A1, A2 depend upon the lengths of the semi axes of the triaxial rigid body.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献