Stability regions in the vicinity of a periodic Ducati orbit

One- and two-dimensional sections of the region of initial conditions in the vicinity of a periodic Ducati orbit have been studied in detail in the plane equal-mass three-body problem. A continuous stability region generated by the periodic Ducati orbit has been revealed. In addition, a number of other stability regions that are probably related to stable hierarchical triple systems have been found. Several specific trajectories from the stability regions and in the boundary zones are analyzed.     

Analog of the surfaces of zero velocity in the restricted elliptic,parabolic, and hyperbolic three-body problem

The surfaces of minimum energy have been constructed in the noncircular restricted three-body problem, which are a generalization of the surfaces of zero velocity known in the circular problem. The Hill stability, conditional stability, and instability criteria have been established. Some astronomical applications of the results obtained are considered.     

Local potential analysis of MHD instability

In many astrophysical problems, the study of the stability of an atmosphere in the presence of a magnetic field is of importance. In most cases the MHD instabilities of atmospheres are studied by energy principle of Bernsteinet al. (1958). In this paper, a general method for studying the stability of a system subject to MHD equations of conditions has been proposed. This is based on the local potential concept put forward by Glansdorff and Prigogine (1964). The scheme for securing stability criteria has been demonstrated in two particular cases.     

Stability of thermonuclear reaction affected by gravitational force

A reaction-diffusion equation describing thermonuclear reaction system affected by gravitational force and temperature gradient is obtained by using the theory of nonequilibrium thermodynamics. We take CNO cycle as an example to investigate the effects of the gravitional force and temperature gradient on the stability of nuclear reaction inside the star. The stability criterion of the stellar structure has been analysed and some attractive results have also been discussed.     

Parallel velocity shear instabilities in an inhomogeneous plasma

The stability of an inhomogeneous anisotropic plasma flowing along a straight magnetic field has been investigated. Both the flow velocity and the plasma density are spatially varying in a direction perpendicular to the magnetic field. The stability of an interface between an inhomogeneous anisotropic plasma flowing along the magnetic field and the non-conducting compressible gas of uniform density flowing parallel to the interface has also been discussed. The effect of gyroviscosity and inhomogeneity on the Kelvin-Helmholtz shear instability has been discussed in certain limiting situations.     

The stability of our solar system

Most investigations of the stability of the solar system have been concerned with the question as to whether the very long term effect of the gravitational attractions of the planets on each other will be to alter the nearly coplanar, nearly circular nature of the orbits in which they move. Analytical investigations in the traditions of Laplace, Lagrange, Poisson and Poincaré strongly indicate stability, though rely on asymptotic expansions with difficult analytical properties. The question is related to the existence of invariant tori, which have been proved to exist in certain motions. Numerical integration experiments have thrown considerable light on possible types of motions, especially in fictitious solar systems in which the planetary masses have been increased to enhance the perturbations, and in testing how critical are stability boundary estimates given by Hill surface type methods.     

Instability of partially-ionized superposed plasmas

The stability of the plane interface separating two viscous superposed partially-ionized plasmas of uniform densities has been studied. The whole system is assumed to be immersed in a uniform two-dimensional horizontal magnetic field and the stability analysis has been carried out through the normal mode technique. The dispersion relation has been derived for the case of two superposed plasmas of equal kinematic viscosities. The dispersion relation has been solved numerically for different values of the physical parameters involved. It is found that viscosity and collision frequency of ionized plasmas both have stabilizing influence on the growth rate of the unstable mode of disturbance.     

The structure and stability of coronal magnetic fields

The high degree of symmetry often assumed in studies of the structure and stability of coronal magnetic field configurations is restrictive and can yield misleading results. We have therefore developed fully three-dimensional numerical methods for constructing force-free equilibria and for examining their stability properties, which make no assumptions about symmetry. A test of the stability analysis has been performed by applying it to the Gold-Hoyle twisted flux tube, which is known to be kink-unstable if the helical field makes more than about one turn between the line-tying end-plates. Our preliminary result is that the critical number of turns is about 1.1, in good agreement with the previous best estimate. However, we find that the growth rate, which has not been discussed previously, is orders of magnitude smaller than expected, even when the flux tube is twisted far beyond the stability limit.     

Non-linear stability in the generalized restricted three-body problem

The non-linear stability of the triangular equilibrium point L ₄ in the generalized restricted three-body problem has been examined. The problem is generalized in the sense that the infinitesimal body and one of the primaries have been taken as oblate spheroids. It is found that the triangular equilibrium point is stable in the range of linear stability except for three mass ratios.     

Stability in the Full Two-Body Problem

Stability conditions are established in the problem of two gravitationally interacting rigid bodies, designated here as the full two-body problem. The stability conditions are derived using basic principles from the N-body problem which can be carried over to the full two-body problem. Sufficient conditions for Hill stability and instability, and for stability against impact are derived. The analysis is applicable to binary small-body systems such as have been found recently for asteroids and Kuiper belt objects.     

无力磁场的稳定性

无力场被广泛用来模拟太阳活动区的强磁场,本文从Bernstein能量原理出发,导出了无力场能量原理的普遍形式,并给出了若干稳定性的充分条件,它们可方便而有效地对无力场进行稳定性判断。     

Rayleigh-Taylor stability in the presence of rotation

The stability of a slab of incompressible fluid with exponentially-increasing density, supported by a semi-infinite homogeneous region and supporting a semi-infinite region of exponentially-decreasing density has been investigated when the whole system rotates uniformly about a vertical axis. The familiar Rayleigh-Taylor stability problems are recovered from the general dispersion relation, both in the presence of rotation and in the absence of rotation.     

Symplectic Mapping for Trojan-Type Motion in the Elliptic Restricted Three-Body Problem

A symplectic mapping for Trojan-type motion has been developed in the secularly changing elliptic restricted three-body problem. The mapping describes well the characteristics of Trojan-type dynamics at small eccentricities. By using this mapping the boundary of the stability region has been studied for different values of the initial eccentricities of hypothetical Jupiter's Trojans. It has been found that in the secularly changing elliptic case the chaotic diffusion at the border of the stability region is stronger than simply in the elliptic case. An explanation of this observation might be the destruction of the chain of islands of the 13:1 secondary resonance between the short and long period component of the Trojan-like motion, caused possibly by the indirect perturbations of Saturn.     

Variational principle for stars with a phase transition

The variational principle for stars with a phase transition has been investigated. The term outside the integral in the expression for the second variation of the total energy of a star is shown to be obtained by passage to the limit from the integration over the region of mixed states in the star. The form of the trial functions ensuring this passage has been found. All of the results have been generalized to the case where general relativity is applicable. The known criteria for the dynamical stability of a star when a new phase appears at its center are shown to follow automatically from the variational principle. Numerical calculations of hydrostatically equilibrium models for hybrid stars with a phase transition have been performed. The form of the trial functions for the second variation of the total energy of a star that describes almost exactly the stability boundaries of such stellar models is proposed.     

Stability criteria for triple stars

A wide variety of equal-mass stellar triple systems has been numerically integrated in order to establish factors pertinent to stability. The significant parameters appear to be whether the relative revolution is direct or retrograde, and the ratio of the periastron distance in the outer orbit to the semi-major axis of the inner orbit. For stability, this ratio must be at least 3.5 for direct orbits and at least 2.75 for retrograde orbits.     

On the stability of high inclination Trojans

Numerical integrations have been performed for orbits of Venus', Earth's and Mars' Trojan-asteroid test particles in a self consistent model of the solar system to study the stability of inclined Trojan orbits. In the case of Mars low inclination orbits tend to be unstable while the contrary seems to apply to Venus and Earth, although the stability of some very high inclination orbits may not be excluded on the basis of these computations.     

Two multiderivate multistep (MDMS) integrators

A preliminary survey of multiderivative multistep integrators is carried out. It is found that all of them are much more accurate than the classical linear multistep methods, but most of them have poor stability. After parameter adjustment, two of them (called MDMS I and MDMS II by us) are competitive with or superior to the classical methods in some aspects, such as accuracy and stability. MDMS I behaves especially well in all the cases which have been studied.     

光纤时间传递系统中时钟驯服模块的设计和实现

提出了一种基于光纤时间传递系统的时钟驯服模块设计方案。介绍了系统硬件的组成。在对信道特性和压控晶振进行理论和实验分析的基础上,设计实现了适用于光纤信道特性的卡尔曼滤波算法以及驯服流程控制程序。实验测试表明：该模块能结合恒温晶振短期稳定度好和光纤时间传递系统秒脉冲长期稳定度好的优点,时间传递的精度优于0．25ns（1σ）,输出的秒脉冲的长期稳定度优于10^-14。     

Linear stability of equilibrium points in the generalized photogravitational Chermnykh’s problem

The equilibrium points and their linear stability has been discussed in the generalized photogravitational Chermnykh’s problem. The bigger primary is being considered as a source of radiation and small primary as an oblate spheroid. The effect of radiation pressure has been discussed numerically. The collinear points are linearly unstable and triangular points are stable in the sense of Lyapunov stability provided μ<μ _Routh =0.0385201. The effect of gravitational potential from the belt is also examined. The mathematical properties of this system are different from the classical restricted three body problem.     

The effect of perturbations in coriolis and centrifugal forces on the nonlinear stability of equilibrium points in the restricted problem of three bodies

Celestial Mechanics and Dynamical Astronomy - The non-linear stability of the equilibrium points in the restricted problem has been studied when small perturbations ε and ε′ are...