共查询到20条相似文献，搜索用时 218 毫秒
1.
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
2.
Boris Garfinkel 《Celestial Mechanics and Dynamical Astronomy》1983,30(4):373-383
In a previous publication (1977) the author has constructed a family () of long-periodic orbits in the Trojan case of the restricted problems of three bodies. Here he constructs the domain of the analytical solution of the problem of the motion, excluding the vicinity of thecritical divisor which vanishes at the exact commensurability of the natural frequencies 1 and 2. In terms of thecritical masses mj(2), or the associatedcritical energies
j
2
(m), is the intersection of the intervals ofshallow resonance, of the form. Inasmuch as the intervals |2–
j
2
|<j ofdeep resonance aredisjoint, it follows that (1) the disjointed family () embraces the tadpole branch, 021, lying in: and (2) despite the clustering of
j
2
(m) atj=, the family () includes, for 2=1, an asymptoticseparatrix that terminates the branch in the vicinity of the Lagrangian pointL
3.In a similar manner, the family () can be extended to the horseshoe branch 1<2
2
2
. 相似文献
3.
A limiting case of the problem of three bodies (m
0,m
1,m
2) is considered. The distance between the bodiesm
0 andm
1 is assumed to be much less than that between their barycenter and the bodym
2 so that one may use Hill's approximation for the potential of interaction between the bodiesm
1 andm
2. In the absence of resonant relations the potential, double-averaged by the mean longitudes ofm
1 andm
2, describes the secular evolution of the orbits in the first approximation of the perturbation theory.As Harrington has shown, this problem is integrable. In the present paper a qualitative investigation of the evolution of the orbits and comparison with the analogous case in the restricted problem are carried out.The set of initial data is found, for which a collision between the bodiesm
0 andm
1 takes place.The region of the parameters of the problem is determined, for which plane retrograde motion is unstable.In a special example the results of approximate analysis are compared with those of numerical integration of the exact equations of the three body problem.
m 0,m 1,m 2. , m 0 m 1. m 2, m 1 m 2 m 1 m 2 . , . . , m 0 m 1. , . .相似文献
4.
P. Brosche 《Astrophysics and Space Science》1977,51(2):401-408
Since the average relation between the angular momentaP and the massesM of galaxies can be represented by a power lawPM
, we can define a relative angular momentum =P/M
(or a constant timeP/M
). For a random motion picture within protogalaxies, should follow a Maxwellian distribution and consequently the dispersion of log should be 0.210.For the reasonable range of (
to 2), the limited sample of galaxies with known dynamical parameters gives between
and 1 times the Maxwellian value. For the plausible special case =2 the reciprocal of the maximum rotational velocityv
m is already a measure of and the larger sample ofv
m-values not only yields the Maxwellian but, moreover, shows the shape of the distribution.
PM , =constP/M . , (lg )=0.210. 7/42, . =2 v m- .相似文献
5.
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
6.
(, 1944; , 1962) . , , . , . , .
Nutational dampers of dual-spin satellites
The paper considers application of the small parameter methods (Artemjev, 1944; Volosov, 1962) in the linear theory of damping the nutating motion of dual-spin satellites. The external moments affecting the satellite are left out of consideration. The influence of the damper on the satellite motion is assumed to be small. As a special case the conditions of stability for the satellite stationary spinning and the optimal parameters ensuring a maximal rate of damping the nutating motion have been obtained.相似文献
7.
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
8.
In this paper we introduce a new parameter, the shear angle of vector magnetic fields, , to describe the non-potentiality of magnetic fields in active regions, which is defined as the angle between the observed vector magnetic field and its corresponding current-free field. In the case of highly inclined field configurations, this angle is approximately equal to the angular shear, , defined by Hagyardet al. (1984). The angular shear, , can be considered as the projection of the shear angle, , on the photosphere. For the active region studied, the shear angle, , seems to have a better and neater correspondence with flare activity than does . The shear angle, , gives a clearer explanation of the non-potentiality of magnetic fields. It is a better measure of the deviation of the observed magnetic field from a potential field, and is directly related to the magnetic free energy stored in non-potential fields. 相似文献
9.
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
10.
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
11.
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
12.
13.
Masaya Saitou 《Astrophysics and Space Science》1989,162(1):47-56
Some peculiarities in the behaviour of a model self-gravitating system described by hydrodynamical equations and isothermal equation of state connected with the presence of thermodynamical fluctuations in real systems were investigated in numerical experiment. The values of density and velocity , , respectively, were computed by numerical code perturbed on each time-step and in each computational cell by random values , for modeling such fluctuations. Perturbed values
i
=
i
+
i
,v
i
=
i
+ v
i
were used to initiate the next step of computations. This procedure is equivalent to an introduction into original hydrodynamical equations of Langevin sources which are random functions. It is shown that these small fluctuations (= v =0,2 =v
2 = 10–8) grow many times in marginally-stable state. 相似文献
14.
G. A. Krasinsky 《Celestial Mechanics and Dynamical Astronomy》1972,6(1):60-83
The general conception of the critical inclinations and eccentricities for theN-planet problem is introduced. The connection of this conception with the existence and stability of particular solutions is established. In the restricted circular problem of three bodies the existence of the critical inclinations is proved for any values of the ratio of semiaxes . The asymptotic behaviour of the critical inclinations as 1 is investigated.
. . . 1.相似文献
15.
, 1-, 2- 3- . , . 相似文献
16.
-- () ., , , , , . , , . , . 相似文献
17.
18.
The process of re-escalation of the scalar field as R
3, the energy density as R
3, and the pressurep aspR
3P, lends itself to obtain a reduced equation that represents, for a wide variety of equations of state, the cosmological evolution of an homogeneous and isotropic, flat Universe. A particular solution to this equation is presented. 相似文献
19.
- . . , . , . 相似文献
20.
, . , , . . . . . , , . 相似文献