scholarly journals On periodic motions of a symmetrical satellite in an orbit with small eccentricity in the case of multiple combinational resonance of the third and fourth orders

2018 ◽  
Vol 28 (3) ◽  
pp. 373-394 ◽  
Author(s):  
A.I. Safonov ◽  
◽  
O.V. Kholostova ◽  
◽  
Keyword(s):  
Periodic Motions ◽  
Small Eccentricity ◽  
The Third

scholarly journals On the Stability of Periodic Motions of a Two-Body SystemWith Flexible Connection in an Elliptical Orbit

2021 ◽  
Author(s):  
Xue Zhong ◽  
Jie Zhao ◽  
Kaiping Yu ◽  
Minqiang Xu
Keyword(s):  
Periodic Solutions ◽  
Fourth Order ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Elliptical Orbit ◽  
Periodic Motions ◽  
Nonlinear Stability Analysis ◽  
The Third ◽  
The Stability ◽  
Lyapunov Instability

Abstract This paper deals with periodic motions and their stability of a flexible connected two-body system with respect to its center of mass in a central Newtonian gravitational field on an elliptical orbit. Equations of motion are derived in a Hamiltonian form and two periodic solutions as well as the necessary conditions for their existence are acquired. By analyzing linearized equations of perturbed motions, Lyapunov instability domains and domains of stability in the first approximation are obtained. In addition, the third and fourth order resonances are investigated in linear stability domains. A constructive algorithm based on a symplectic map is used to calculate the coeffcients of the normalized Hamiltonian. Then a nonlinear stability analysis for two periodic solutions is performed in the third and fourth order resonance cases as well as in the nonresonance case.

scholarly journals On the Dynamics of a Gravitational Dipole

2021 ◽  
Vol 17 (3) ◽  
pp. 247-261
Author(s):  
A. P. Markeev ◽  
Keyword(s):  
Nonlinear Oscillations ◽  
Initial Conditions ◽  
Nonlinear Approximation ◽  
Center Of Mass ◽  
Kam Theory ◽  
Computer Algorithms ◽  
Periodic Motions ◽  
Small Eccentricity ◽  
Formal Stability ◽  
Nominal Mode

The main purpose of this paper is to investigate nonlinear oscillations of the gravitational dipole in a neighborhood of its nominal mode. The orbit of the center of mass is assumed to be circular or elliptic with small eccentricity. Consideration is given both to planar and arbitrary spatial deviations of the gravitational dipole from its position corresponding to the nominal mode. The analysis is based on the classical Lyapunov and Poincaré methods and the methods of Kolmogorov – Arnold – Moser (KAM) theory. The necessary calculations are performed using computer algorithms. An analytic representation is given for conditionally periodic oscillations. Special attention is paid to the problem of the existence of periodic motions of the gravitational dipole and their Lyapunov stability, formal stability (stability in an arbitrarily high, but finite, nonlinear approximation) and stability for most (in the sense of Lebesgue measure) initial conditions.

BIFURCATIONS FROM PLANAR TO THREE-DIMENSIONAL PERIODIC ORBITS IN THE PHOTO-GRAVITATIONAL RESTRICTED FOUR-BODY PROBLEM

2008 ◽  
Vol 18 (02) ◽  
pp. 465-479 ◽  
Author(s):  
T. J. KALVOURIDIS ◽  
K. G. HADJIFOTINOU
Keyword(s):  
Periodic Orbits ◽  
Three Dimensional ◽  
Periodic Motions ◽  
Critical Stability ◽  
Third Body ◽  
Small Particles ◽  
The Third ◽  
Gravitational Forces ◽  
Radiation Sources ◽  
Four Body Problem

We study the bifurcations of three-dimensional periodic motions from two-dimensional orbits of small particles in the neighborhood of a system that consists of three major bodies being always in syzygy. We assume that two of them have equal masses and are located at equal distances from the third body which has a different mass. All or some of the primaries are radiation sources and therefore apart from gravitational forces, we also consider forces that result from radiation. We apply the method of vertical critical stability in order to find the families of three-dimensional periodic orbits that bifurcate from families of planar periodic motions. Consequently, we study the parametric variations of the bifurcation points.

Progress report on 21-cm observations at low latitude between longitudes (l 11) 0° and 66°

1967 ◽  
Vol 31 ◽  
pp. 177-179
Author(s):  
W. W. Shane
Keyword(s):  
Preliminary Report ◽  
Progress Report ◽  
Galactic Centre ◽  
Low Latitude ◽  
The Third ◽  
Introductory Lecture ◽  
Centre Region

In the course of several 21-cm observing programmes being carried out by the Leiden Observatory with the 25-meter telescope at Dwingeloo, a fairly complete, though inhomogeneous, survey of the regionl11= 0° to 66° at low galactic latitudes is becoming available. The essential data on this survey are presented in Table 1. Oort (1967) has given a preliminary report on the first and third investigations. The third is discussed briefly by Kerr in his introductory lecture on the galactic centre region (Paper 42). Burton (1966) has published provisional results of the fifth investigation, and I have discussed the sixth in Paper 19. All of the observations listed in the table have been completed, but we plan to extend investigation 3 to a much finer grid of positions.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

Monte Carlo Algorithms for Moments of Transition Arrays

1988 ◽  
Vol 102 ◽  
pp. 79-81
Author(s):  
A. Goldberg ◽  
S.D. Bloom
Keyword(s):  
Monte Carlo ◽  
State Vector ◽  
Basis Vector ◽  
Collective State ◽  
Dispersion Characteristics ◽  
Dipole Strength ◽  
The Third ◽  
Monte Carlo Algorithms ◽  
Third Moment ◽  
Very High

AbstractClosed expressions for the first, second, and (in some cases) the third moment of atomic transition arrays now exist. Recently a method has been developed for getting to very high moments (up to the 12th and beyond) in cases where a “collective” state-vector (i.e. a state-vector containing the entire electric dipole strength) can be created from each eigenstate in the parent configuration. Both of these approaches give exact results. Herein we describe astatistical(or Monte Carlo) approach which requires onlyonerepresentative state-vector |RV> for the entire parent manifold to get estimates of transition moments of high order. The representation is achieved through the random amplitudes associated with each basis vector making up |RV>. This also gives rise to the dispersion characterizing the method, which has been applied to a system (in the M shell) with≈250,000 lines where we have calculated up to the 5th moment. It turns out that the dispersion in the moments decreases with the size of the manifold, making its application to very big systems statistically advantageous. A discussion of the method and these dispersion characteristics will be presented.

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

The effects of Cyclosporin-A (CYA) on the Ultrastructure of Gingival Mast Cells (GMC) in Behcet's disease (BD)

1990 ◽  
Vol 48 (3) ◽  
pp. 358-359
Author(s):  
Oktay Arda ◽  
Ulkü Noyan ◽  
Selgçk Yilmaz ◽  
Mustafa Taşyürekli ◽  
İsmail Seçkin ◽  
...  
Keyword(s):  
Unknown Etiology ◽  
Control Group ◽  
Target Cells ◽  
Gingival Hyperplasia ◽  
Cellular Activity ◽  
Direct Relation ◽  
Immune Disease ◽  
Genital Ulceration ◽  
Functional Changes ◽  
The Third

Turkish dermatologist, H. Beheet described the disease as recurrent triad of iritis, oral aphthous lesions and genital ulceration. Auto immune disease is the recent focus on the unknown etiology which is still being discussed. Among the other immunosupressive drugs, CyA included in it's treatment newly. One of the important side effects of this drug is gingival hyperplasia which has a direct relation with the presence of teeth and periodontal tissue. We are interested in the ultrastructure of immunocompetent target cells that were affected by CyA in BD.Three groups arranged in each having 5 patients with BD. Control group was the first and didn’t have CyA treatment. Patients who had CyA, but didn’t show gingival hyperplasia assembled the second group. The ones displaying gingival hyperplasia following CyA therapy formed the third group. GMC of control group and their granules are shown in FIG. 1,2,3. GMC of the second group presented initiation of supplementary cellular activity and possible maturing functional changes with the signs of increased number of mitochondria and accumulation of numerous dense cored granules next to few normal ones, FIG. 4,5,6.

Effects of Phonological Decoding Training on Children's Word Recognition of CVC, CV, and VC Structures

1996 ◽  
Vol 5 (1) ◽  
pp. 67-78 ◽  
Author(s):  
Kenyatta O. Rivers ◽  
Linda J. Lombardino ◽  
Cynthia K. Thompson
Keyword(s):  
Word Recognition ◽  
Multiple Baseline ◽  
Single Subject ◽  
Group Training ◽  
Complex Structures ◽  
Multiple Baseline Design ◽  
Baseline Design ◽  
Phonological Decoding ◽  
The Third ◽  
Letter Sound

The effects of training in letter-sound correspondences and phonemic decoding (segmenting and blending skills) on three kindergartners' word recognition abilities were examined using a single-subject multiple-baseline design across behaviors and subjects. Whereas CVC pseudowords were trained, generalization to untrained CVC pseudowords, untrained CVC real words, untrained CV and VC pseudowords, and untrained CV and VC real words were assessed. Generalization occurred to all of the untrained constructions for two of the three subjects. The third subject did not show the same degree of generalization to VC pseudowords and real words; however, after three training sessions, this subject read all VC constructions with 100% accuracy. Findings are consistent with group training studies that have shown the benefits of decoding training on word recognition and spelling skills and with studies that have demonstrated the effects of generalization to less complex structures when more complex structures are trained.

Sign in / Sign up

Export Citation Format

Share Document