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1.
The location and the stability of the libration points in the restricted problem have been studied when small perturbation and are given to the Coriolis and the centrifugal forces respectively. It is seen that the pointsL
4 andL
5 form nearly equilateral triangles with the primaries and the pointsL
1,L
2,L
3 remain collinear. It is further observed that for the pointsL
4 andL
5, the range of stability increases or decreases depending upon whether the point (, ) lies in one or the other of the two parts in which the (, ) plane is divided by the line 36-19=0 and the stability of the collinear points is not influenced by the perturbations and they remain unstable. 相似文献
2.
E. E. Shnol 《Celestial Mechanics and Dynamical Astronomy》1984,33(2):159-167
The equilibrium point O of an autonomous Hamiltonian system of two degrees of freedom is considered for small-oscillation frequencies related as 2=21+. If under the precise resonance (=0) the equilibrium is unstable, the inner diameter () of the domain of stability containing the point O is estimated. It is shown that for the normalized variables ()/b where b is the corresponding resonance coefficient. The estimates () for other main resonances are reported. 相似文献
3.
W. E. Alnaser 《Earth, Moon, and Planets》1990,48(2):177-181
The clear sky emissivity 0 and the ground emissivity
g
in Bahrain is studied. The study reveals that the annual value of 0 is 0.88 ± 0.039 relating to the maximum and the minimum values in August and February, respectively. Meanwhile, the annual value of
g
is 0.338 ± 0.228, where the maximum and the minimum values are in July and January, respectively. These two parameters are related to the transmittance factor . 相似文献
4.
The effect of small perturbations and in the coriolis and the centrifugal forces respectively on the stability of the triangular points in the restricted problem of three bodies with variable mass has been studied. It is found that the range of stability of triangular points increases or decreases depending upon whether the perturbation point (, ) lies in one or the other of the two parts in which the (, ) plane is divided by the line J8–J9=0 where J8 and J9 depend upon , the constant due to the variation in mass governed by Jeans' law. 相似文献
5.
S. Selak 《Astrophysics and Space Science》1989,159(1):153-156
In this Letter we propose to consider the four-energy-space whose coordinates are composed as follows: (i) the coordinate 0 refers to the internal energy of the body (it is involved as an unknown function of the rest-energy and the kinetic energy of the body), and (ii) the coordinates 1, 2, 3 relate to the presence of gravitational, electromagnetic, and thermal energy at the location of the body respectively. We involve yet the proper energy interval d2 by analogy to the four-interval ds
2 in general relativity. From such metric field we calculate the Ricci tensor in the simplest case. In addition, we require its form to be the same one as that considered by Schwarzschild. Comparing both solutions we obtain Einstein's relationE=mc
2. 相似文献
6.
A family of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form H=A+B was given in (McLachlan, 1995). We give here a constructive proof that for all integer p, such integrator exists, with only positive steps, and with a remainder of order O(p + 22), where is the stepsize of the integrator. Moreover, we compute the analytical expressions of the leading terms of the remainders at all orders. We show also that for a large class of systems, a corrector step can be performed such that the remainder becomes O(p +42). The performances of these integrators are compared for the simple pendulum and the planetary three-body problem of Sun–Jupiter–Saturn. 相似文献
7.
In the theory of supergravity (N=1), the supersymmetric version of general relativity, and for the Kasner cosmological model (Bianchi type I) we find a non-trivial solution (for the metric and spinor-vector) under the most simple assumption =11 + 22; 12+21=0 and for a special choosed gaugeN=1,N
j=0, 0=0. This method could be also applied to other cosmological metrics and extended to enlarged Grassmann basis.O. Obregón was partially supported by the Alexander von Humboldt Stiftung. 相似文献
8.
A model of a first generation intermediate star of 5M
, with Z=0 has been considered. The model is at an advanced stage of its evolution and has a double shell burning. It burns helium in the inner shell, and hydrogen, via CNO cycle, in the outer shell.
=(log/log)
T
and
T
=(log/logT)
were computed allowing for the oscillations of the relative mass abundance of the reagents in nuclear reactions. Including
=(log/log)
T
and
=(log/logT)
of mean molecular weight and the effect of the oscillations of abundances due to nuclear reactions, stability was studied. Contrary to the results of the static calculations, we found that instability due to the excitation mechanism provided by the high temperature sensitivity of energy generation rate propagates up to the surface. Thus the model in question was found to be unstable against radial adiabatic pulsations, in its fundamental mode. 相似文献
9.
The nonlinear evolution of waves in a low-density plasma in a strong magnetic field is investigated on the basis of the Chew-Goldberger-Low approximation. The nonlinear effects are found to be essentially different for the magneto-acoustic and Alfvén modes. For the magnetic-acoustic mode, waveform distortion occurs at order 2 (where is a measure of the linear wave amplitude) and shock formation occurs over a time-scale of order –1. For the Alfvén wave, modulation occurs at order 3 and shock formation over a time-scale of order –2. The nature of the waveform distortion is qualitatively different for the two modes. 相似文献
10.
The stability properties of the collisionless plasma and encounterless stellar gas described by the Vlasov equations are studied. The introduction of the multiple Water Bag model allows, for one-dimensional plane geometry, a treatment of the general case and removes some of the difficulties connected with the formulation of the energy variation. From this last result it can be deduced that both plasma and stellar systems steady state described by a monotonically decreasing distributionF() are stable. The demonstration is extended to the spherically symmetric case for self-gravitating gas. Next the constraint of a monotonically decreasingF() is relaxed and it is supposed that the instability appears through the point =0. This is known to be true for some type of plasma instabilities (two streams) but is a simple working hypothesis in the gravitational case. For this marginal mode theN bags equations degenerate into a single wave equation and the stability of the system is given by the sign of the eigenvalues of a Schroedinger type operator. A simple physical picture is obtained for the plasma case where the quantitity (dF/d) dV (the square of the local maximum wavenumber of instability) is introduced. A virtual variation of this quantity indicates if the initial steady state was stable or unstable. 相似文献
11.
M. Caputo 《Celestial Mechanics and Dynamical Astronomy》1985,36(4):375-390
The tidal field caused by the second order zonal harmonic of the gravitational field of a planet is discussed according to the fernwirkungsgesetz (principle of local action) of Weyl (1921) introducing an accurate and simple form of the gravitational potential of the planet in elliptic coordinates. It is seen that the tidal field can be described at each point as a small rotation of the local canonical frame which causes a libration and a precession of the axis of rotation of the satellites of the planet. It is also shown that at each point P, is one third of the angle between the line of force through P and the line from P to the center of mass of the planet. All the formulae obtained, to compute and , are in closed form. 相似文献
12.
In this paper we consider almost integrable systems for which we show that there is a direct connection between symplectic methods and conventional numerical integration schemes. This enables us to construct several symplectic schemes of varying order. We further show that the symplectic correctors, which formally remove all errors of first order in the perturbation, are directly related to the Euler—McLaurin summation formula. Thus we can construct correctors for these higher order symplectic schemes. Using this formalism we derive the Wisdom—Holman midpoint scheme with corrector and correctors for higher order schemes. We then show that for the same amount of computation we can devise a scheme which is of order O(h
6)+(2
h
2), where is the order of perturbation and h the stepsize. Inclusion of a modified potential further reduces the error to O(h
6)+(2
h
4).This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
13.
Ian W. Walker A. Gordon Emslie Archie E. Roy 《Celestial Mechanics and Dynamical Astronomy》1980,22(4):371-402
An expansion of the force function ofn-body dynamical systems, where the equations of motion are expressed in the Jacobian coordinate system, is shown to give rise naturally to a set of (n–1) (n–2) dimensionless parameters
ki
li
{i = 2,...,n;k = 2,...,i – 1 (i 3);l =i + 1,...,n (i n – 1)}, representative of the size of the disturbances on the Keplerian orbits of the various bodies. The expansion is particularized to the casen=3 which involves the consideration of only two parameters
23 and
32. Further, the work of Szebehely and Zare (1977) is reviewed briefly with reference to a sufficient condition for the stability of corotational coplanar three-body systems, in which two of the bodies form a binary system. This condition is sufficient in the sense that it precludes any possibility of an exchange of bodies, i.e. Hill type stability, however, it is not a necessary condition. These two approaches are then combined to yield regions of stability or instability in terms of the parameters
23 and
32 for any system of given masses and orbital characteristics (neglecting eccentricities and inclinations) with the following result: that there is a readily applicable rule to assess the likelihood of stability or instability of any given triple system in terms of
23 and
32.Treating a system ofn bodies as a set of disturbed three-body systems we use existing data from the solar system, known triple systems and numerical experiments in the many-body problem to plot a large number of triple systems in the
23,
32 plane and show the results agree well with the
23,
32 analysis above (eccentricities and inclinations as appropriate to most real systems being negligible). We further deal briefly with the extension of the criteria to many-body systems wheren>4, and discuss several interesting cases of dynamical systems. 相似文献
14.
Masanori Yoshizawa Shunsaku Suzuki Rikinosuke Fukaya 《Astrophysics and Space Science》1991,177(1-2):41-45
The catalog of positions of 1007 stars (792 FK4 and FK4S stars, 57 OB stars, 49 NPZT stars, and 109 SAO stars) is presented. They were observed during the period from December 1984 to September 1985 with the Tokyo Photoelectric Meridian Circle (Tokyo PMC). The positions in the catalog are referred to the equinox and equator of J2000, and are based on the FK4 system. The internal errors of a single observation were estimated to be (
cos,
)=(0.16, 0.19), whereas the mean internal errors of the catalog positions were (0.08, 0.08) for FK4 stars and (0.09, 0.11) for FK4S stars. A comparison of the positions of the FK4 stars in the present catalog with those of the FK4 catalog shows significant differences
cos and
in some declination zones. Some of those differences are commonly found in other recent catalogs. Thus they may be considered to be real systematic errors in the FK4 system. Neither significant magnitude nor color equations exist in the Tokyo PMC 85 catalog. 相似文献
15.
The emission spectra and their time variations of gyro-synchrotron emission from an ensemble of energetic electrons are computed for some initial power-law distributions of the electron energies N()d=
–
with =2 or 4. The spectra and decay curves of the emission are compared with solar microwave bursts in order to separately estimate the magnetic field H and . From a limited number of observations, we have 3 and H 103 gauss for the microwave impulsive bursts, and 2 and H (500–1000) gauss for the microwave type-IV bursts. 相似文献
16.
Vittorio Coti Zelati 《Celestial Mechanics and Dynamical Astronomy》1989,46(2):177-186
We prove existence and multiplicity of T-periodic solutions (for any given T) for the N-body problem in
m
(any m 2) where one of the bodies has mass equal to 1 and the others have masses 2,...,
N
, small. We find solutions such that the body of mass 1 moves close to x = 0 while the body of mass i moves close to one of the circular solutions of the two body problem of period T/k
i, where ki is any odd number. No relation has to be satisfied by k
2,...,k
N. 相似文献
17.
G. Contopoulos H. Papadaki C. Polymilis 《Celestial Mechanics and Dynamical Astronomy》1994,60(2):249-271
We study the structure of chaos in a simple Hamiltonian system that does no have an escape energy. This system has 5 main periodic orbits that are represented on the surface of section
by the points (1)O(0,0), (2)C
1,C
2(±y
c, 0), (3)B
1,B
2(O,±1) and (4) the boundary
. The periodic orbits (1) and (4) have infinite transitions from stability (S) to instability (U) and vice-versa; the transition values of are given by simple approximate formulae. At every transitionS U a set of 4 asymptotic curves is formed atO. For larger the size and the oscillations of these curves grow until they destroy the closed invariant curves that surroundO, and they intersect the asymptotic curves of the orbitsC
1,C
2 at infinite heteroclinic points. At every transitionU S these asymptotic curves are duplicated and they start at two unstable invariant points bifurcating fromO. At the transition itself the asymptotic curves fromO are tangent to each other. The areas of the lobes fromO increase with ; these lobes increase even afterO becomes stable again. The asymptotic curves of the unstable periodic orbits follow certain rules. Whenever there are heteroclinic points the asymptotic curves of one unstable orbit approach the asymptotic curves of another unstable orbit in a definite way. Finally we study the tangencies and the spirals formed by the asymptotic curves of the orbitsB
1,B
2. We find indications that the number of spiral rotations tends to infinity as . Therefore new tangencies between the asymptotic curves appear for arbitrarily large . As a consequence there are infinite new families of stable periodic orbits that appear for arbitrarily large . 相似文献
18.
K. S. Krishna Swamy 《Astrophysics and Space Science》1970,8(1):86-89
Two hyades giant stars, and Tau, have been studied from an analysis of strong line profiles. We get for Tau,T
e
=4750K and logg=2.7, and for Tau,T
e
=4700K and logg=2.8. Hydrogen-to-metal ratio for the two stars is nearly the same as that of solar value. 相似文献
19.
G. Contopoulos 《Celestial Mechanics and Dynamical Astronomy》1986,38(1):1-22
We study the bifurcations of families of double and quadruple period orbits in a simple Hamiltonian system of three degrees of freedom. The bifurcations are either simple or double, depending on whether a stability curve crosses or is tangent to the axis b=–2. We have also generation of a new family whenever a given family has a maximum or minimum or .The double period families bifurcate from simple families of periodic orbits. We construct existence diagrams to show where any given family exists in the control space (, ) and where it is stable (S), simply unstable (U), doubly unstable (DU), or complex unstable (), We construct also stability diagrams that give the stability parameters b1 and b2 as functions of (for constant ), or of (for constant ).The quadruple period orbits are generated either from double period orbits, or directly from simple period orbits (at double bifurcations). We derive several rules about the various types of bifurcations. The most important phenomenon is the collision of bifurcations. At any such collision of bifurcations the interconnections between the various families change and the general character of the dynamical system changes. 相似文献
20.
Srinivas N. Mohan Ph.D. Candidate Dept. of Aeronautics Astronautics John V. Lange Benjamin O. Lange 《Celestial Mechanics and Dynamical Astronomy》1972,5(2):157-173
Interaction between orbital motion and attitude libration dynamics of an arbitrary rigid body moving in a central Newtonian field is considered to second order. Advantage is taken of the decoupling between inplane-pitch and roll-yaw out-of-plane motion to restrict the motion to the orbital plane by an appropriate choice ofinitial conditions. An averaged solution to the nonlinear inplane-pitch equations whose accuracy is determined by ignoring terms of order {·G32/a
2, 2,2,G32/a
2} and higher is presented. The results show that the near-resonant motion is characterized by a periodic interchange of energy between the attitude and orbital motion.Associate Professor, Department of Aeronautics and Astronautics. 相似文献