共查询到20条相似文献，搜索用时 359 毫秒
1.
Alexandre Pousse Philippe Robutel Alain Vienne 《Celestial Mechanics and Dynamical Astronomy》2017,128(4):383-407
In the framework of the planar and circular restricted three-body problem, we consider an asteroid that orbits the Sun in quasi-satellite motion with a planet. A quasi-satellite trajectory is a heliocentric orbit in co-orbital resonance with the planet, characterized by a nonzero eccentricity and a resonant angle that librates around zero. Likewise, in the rotating frame with the planet, it describes the same trajectory as the one of a retrograde satellite even though the planet acts as a perturbator. In the last few years, the discoveries of asteroids in this type of motion made the term “quasi-satellite” more and more present in the literature. However, some authors rather use the term “retrograde satellite” when referring to this kind of motion in the studies of the restricted problem in the rotating frame. In this paper, we intend to clarify the terminology to use, in order to bridge the gap between the perturbative co-orbital point of view and the more general approach in the rotating frame. Through a numerical exploration of the co-orbital phase space, we describe the quasi-satellite domain and highlight that it is not reachable by low eccentricities by averaging process. We will show that the quasi-satellite domain is effectively included in the domain of the retrograde satellites and neatly defined in terms of frequencies. Eventually, we highlight a remarkable high eccentric quasi-satellite orbit corresponding to a frozen ellipse in the heliocentric frame. We extend this result to the eccentric case (planet on an eccentric motion) and show that two families of frozen ellipses originate from this remarkable orbit. 相似文献
2.
Third-order virial equations are used to investigate the oscillations and the stability of the sequence of uniformly rotating compressible Maclaurin spheroids, referred to in an inertial frame. It is seen that in the case of the oscillations belonging to the third harmonics, the frequency spectrum of the Maclaurin sequence referred to in an inertial frame is distinct from the spectrum of the Maclaurin sequence considered stationary in a rotating frame of reference. Considering the Maclaurin sequence in an inertial frame, the neutral point and the point of onset of dynamical instability (corresponding to the third harmonic deformations) are isolated. They occur for the values of the eccentricitye=0.73113 and 0.96696, respectively. The neutral point is the analogue of the first point of bifurcation along the Dedekind sequence of ellipsoids and is distinct from the neutral point (e=0.89926) along the Maclaurin sequence considered stationary in a rotating frame; this latter point is the analogue of the first point of bifurcation along the Jacobian sequence. Both the Maclaurin sequences in an inertial frame and in a rotating frame become, however, dynamically unstable for the same eccentricitye=0.96696. 相似文献
3.
Renato Calleja Eusebius Doedel Carlos García-Azpeitia 《Celestial Mechanics and Dynamical Astronomy》2018,130(7):48
We use numerical continuation and bifurcation techniques in a boundary value setting to follow Lyapunov families of periodic orbits and subsequently bifurcating families. The Lyapunov families arise from the polygonal equilibrium of n bodies in a rotating frame of reference. When the frequency of a Lyapunov orbit and the frequency of the rotating frame have a rational relationship, then the orbit is also periodic in the inertial frame. We prove that a dense set of Lyapunov orbits, with frequencies satisfying a diophantine equation, correspond to choreographies. We present a sample of the many choreographies that we have determined numerically along the Lyapunov families and along bifurcating families, namely for the cases \(n=3\), 4, and 6–9. We also present numerical results for the case where there is a central body that affects the choreography, but that does not participate in it. Animations of the families and the choreographies can be seen at the link below. 相似文献
4.
I. Stellmacher 《Celestial Mechanics and Dynamical Astronomy》1982,28(4):381-400
In a previous paper (Stellmacher, 1981, hereafter mentioned as Paper I), we have given an algorithm for the construction of periodic orbits in a rotating frame, for satellites around an oblate planet. In the present paper, we apply this theory to the Mimas-Tethys case; we obtain the following results:
- Without resonance, it is possible to find a rotating system in which the solution is a periodic one. The angular velocity of this rotating frame is calculated as function of the masses of the two satellites.
- Including the resonant terms and assuming an exact commensurability of the implied frequencies, we demonstrate that the condition for periodic solutions in the rotating system as defined in (a) is: the initial position of the satellites at conjunction lies on an axis defined by (Ω1+Ω2)/2 or (Ω1+Ω2)/2 + π/2;Ω1 and Ω2 are the longitudes of the ascending nodes of the satellite's orbits. The solution still is a periodic one, thus all the conjunction occur in either axis.
- In the Mimas Tethys case there is only approximately commensurability between these frequencies. The two satellites are considered as oscillators whose amplitudes and phases are functions of time. The equation of the libration can be established; we find the usual form, but for each satellite the generating solution is a periodic solution (as defined in Paper I), but not a Keplerian one. It follows a determination of the masses which slightly differs from that given by Kozai (1957), when the same values of the observed quantities are used for calculations.
- The equation of the libration is: $$\ddot z + n_1^2 h^2 \sin z + n_1 q\dot z\sin z = 0$$
5.
Witold Maciejewski E. Athanassoula 《Monthly notices of the Royal Astronomical Society》2007,380(3):999-1008
Bars in galaxies are mainly supported by particles trapped around stable periodic orbits. These orbits represent oscillatory motion with only one frequency, which is the bar driving frequency, and miss free oscillations. We show that a similar situation takes place in double bars: particles get trapped around parent orbits, which in this case represent oscillatory motion with two frequencies of driving by the two bars, and which also lack free oscillations. Thus the parent orbits, which constitute the backbone of an oscillating potential of two independently rotating bars, are the double-frequency orbits. These orbits do not close in any reference frame, but they map on to closed curves called loops. Trajectories trapped around the parent double-frequency orbit map on to a set of points confined within a ring surrounding the loop. 相似文献
6.
In most courses on continuum mechanics the law of angular momentum is studied about a fixed point (usually about the origin of the frame). In this article we clarify this law about any point in three-dimensional Euclidean space and discuss the law, about any point, for an observer in a rotating frame. 相似文献
7.
O. Kaburaki 《Astrophysics and Space Science》1985,112(2):287-301
An example of the self-consistent solution which belongs to the non-trivial solution, obtained in a previous paper (Kaburaki, 1985), is found in a nearly co-rotating inner magnetosphere. Though the stellar wind is neglected there compared with the co-rotatinal velocity, drift motion around the magnetic axis, which is a manifestation of inertial effects, is determined self-consistently with the electromagnetic field. In this process, explicit expressions for the energy integral in the rotating frame and for the density distribution are also obtained. These expressions contain a fundamental length, which is to be evaluated according to physical conditions of a magnetosphere and determines the asymptotic-kinetic energy of a plasma particle at infinity. The electric current associated with the drift motion is too small to alter the original magnetic field, but the electric field is modified by the inertial effects even in the inner magnetosphere. The integrated Ohm's law is used to describe a force balance in the rotating frame, in the limits of weak and strong magnetic field. 相似文献
8.
When assessing the influence of the Coriolis force on wave propagation in plasmas or other dielectric media, all the equations and relevant physical quantitities should be expressed in a rotating reference frame. Only then does the Coriolis force appear. However, most treatments for plasmas seem to fail in this respect because the Maxwell equations are used in their customary form, which in general is not valid in a rotating frame. A consistent approach requires the inclusion of Schiff charges and currents in the Maxwell equations. These Schiff sources are fictitious in the same way as the Coriolis force. The resulting wave equation has coefficients depending on the position and this precludes a plane wave solution, even in the slow rotation approximation where the centrifugal force may be neglected in comparison with the Coriolis force. Perturbation analysis then gives a dispersion law as if the system were not rotating. The wave electric field, however, now has a position dependent amplitude, which is not only stretched but also changed in direction compared to the previously known unperturbed or not rotating solution. 相似文献
9.
The Eulerian equations are set up for a model subject to homoaxial rotation and suitable for simulation of a non-uniformly rotating star. These equations are formulated in a non-inertial frame of reference, rotating uniformly (i.e., rigidly) with respect to the inertial common frame. 相似文献
10.
W. Wiesel 《Celestial Mechanics and Dynamical Astronomy》1980,21(3):265-279
The periodic orbit representing the motion of the inner three Galilean satellites of Jupiter is constructed in a rotating frame. Stability analysis indicates linear instability; but the repeated Poincaré exponents are associated with time and rotational symmetries, and it is concluded that the system is orbitally stable. Analysis of system frequencies reveals two resonances with the Sun. The rotation rate of the reference frame is close to 8910 the mean motion of Jupiter, and the period of the reference orbit is nearly 1710446 the period of Jupiter. The 8910 resonance is investigated via the method of averaging. The Jovian system currently circulates just outside the capture boundary with a period of about 117000 year, but with rotation rate of the reference frame varying by over an order of magnitude. Including tidal interaction, the system is evolving towards temporary capture in this resonance. 相似文献
11.
G.Z. Machabeli G.Z. Mchedlishvili D.E. Shapakidze 《Astrophysics and Space Science》2000,271(3):277-292
A simple mechanichal problem of the force-free motion of a relativistic bead inside a rotating pipe is examined. A relevant change of shape of the pipe is considered. The
force-free motion of the bead along the rotating pipe is examined as the motion in a differentially rotating medium. The differential
rotation proves to be resembling a well known case of the Couette flow without outer cylinder. The determination of vectoral fields (magnetic field) in the rotating charged mediums (plasma) is
problematic for the laboratory observer. Therefore the same problem is examined in the framework of general relativity, that is the physical quantities are considered in the inertial frame and non-inertial frame with no rotational in homogeneity.
The problematic character of the determination of the physical quantity in the differentially rotating madium relative to
the inertial observer is explained. It is shown that at certain large distances from the rotation center the pipe does not
rotate. However, at rather small distances its shape takes on the appearance of an expanded spiral-like configuration. A possible relevance of the obtained results to the motion of a relativistic plasma flows in pulsar magnetosphere
is pointed out. The areas of Crab pulsar's dipole radiation are estimated.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
12.
V. S. Geroyannis 《Astrophysics and Space Science》1985,114(1):175-189
In this paper the ‘class of near homoaxial rotations’ is defined, being suitable for treatment of problems of nonuniform rotation
of stars. This class is represented by a proper form of the so-called ‘velocity tensor’, the latter describing efficiently
the motion of a deformable finite material continuum in the common frame. The ‘class of particular near homoaxial rotations’
is then defined, characterized by simple transformation equations of the velocity tensor in two noninertial frames; namely,
in a ‘frame rotating uniformly’ relative to the common frame, and in a ‘frame rotating nonuniformly’ relative to it. A sufficient
condition is also derived so that a near homoaxial rotation be reducible to a particular one. ‘Preferred frames’ are then
defined in the sense that they preserve a near homoaxial rotation in its class when referring thismotion; that is, such frames
keep invariant the intertial class of the motion. Finally, a method is proposed for constructing a nonuniformly rotating preferred
frame, to which a near homoaxial rotation is referred simply as ‘radial distortion’. 相似文献
13.
Chang-Sheng Shi College of Material Science Chemical Engineering Hainan University Hainan China Key Laboratory of Modern Astronomy Astrophysics Nanjing University Nanjing 《中国天文和天体物理学报》2011,(11)
We discuss the modes of the Alfve'n waves in the accretion disk with a toroidal magnetic field in black hole low mass X-ray binaries in a rotating frame.By solving the perturbed general relativistic magnetohydrodynamic equations in the rotating frame,we find two stable modes of the Alfve'n wave which are the same as those in the fiducial observer frame.This gives a feasible way to transform between the two different frames,which validates the possible Alfve'n wave modes in the accreting celestial bodies wit... 相似文献
14.
Colin R. Mcinnes 《Celestial Mechanics and Dynamical Astronomy》1997,67(2):167-180
The two-body problem is considered with an additional thrust induced acceleration. Stationary solutions are obtained to this
problem in a rotating frame of reference which generates families of displaced circular orbits when viewed from an internal
frame of reference. The existence and stability of these orbits is considered along with applications such as in-situ observations
of Saturn's ring system and spacecraft proximity operations.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
15.
Slawomir Breiter Krzysztof Langner 《Celestial Mechanics and Dynamical Astronomy》2017,128(2-3):323-342
Kustaanheimo–Stiefel (KS) transformation depends on the choice of some preferred direction in the Cartesian 3D space. This choice, seldom explicitly mentioned, amounts typically to the direction of the first or the third coordinate axis in Celestial Mechanics and atomic physics, respectively. The present work develops a canonical KS transformation with an arbitrary preferred direction, indicated by what we call a defining vector. Using a mix of vector and quaternion algebra, we formulate the transformation in a reference frame independent manner. The link between the oscillator and Keplerian first integrals is given. As an example of the present formulation, the Keplerian motion in a rotating frame is re-investigated. 相似文献
16.
The dynamics of a charged relativistic particle in electromagnetic field of a rotating magnetized celestial body with the magnetic axis inclined to the axis of rotation is studied. The covariant Lagrangian function in the rotating reference frame is found. Effective potential energy is defined on the base of the first integral of motion. The structure of the equipotential surfaces for a relativistic charged particle is studied and depicted for different values of the dipole moment. It is shown that there are trapping regions for the particles of definite energies. 相似文献
17.
Basic formulas of discrete mechanics in a rotating frame of references are obtained. Its application to several computer examples of orbits near by the equilibrium points of the Earth-Moon system are presented, and—for computational purposes—an algorithm is given. 相似文献
18.
C.A. Jones P. Boronski A.S. Brun G.A. Glatzmaier T. Gastine M.S. Miesch J. Wicht 《Icarus》2011,216(1):120-135
Benchmark solutions for fully nonlinear anelastic compressible convection and dynamo action in a rotating spherical shell are proposed. Three benchmarks are specified. The first is a purely hydrodynamic case, which is steady in a uniformly drifting frame. The second is a self-excited saturated dynamo solution, also steady in a drifting frame. The third is again a self-excited dynamo but is unsteady in time, and it has a higher Rayleigh number than the steady dynamo benchmark. Four independent codes have been tested against these benchmarks, and very satisfactory agreement has been found. This provides an accurate reference standard against which new anelastic codes can be tested. 相似文献
19.
O. Kaburaki 《Astrophysics and Space Science》1985,112(1):157-174
A theoretical scheme is developed to deal with the problems of stellar winds in three-dimensional situations, and relativistic fluid equations are integrated formally under isentropic and quasi-stationary conditions, in a flat space-time.The relativistic Euler equation for a one-component plasma is expressed in the same form as the ideal-MHD condition for the effective electromagnetic field which combines the inertial and pressure terms with the true electromagnetic field. This equation and that of mass continuity are integrated formally by introducing Euler-type potentials for the effective magnetic field and for the mass flux in the rotating frame, respectively. Functional form of one of these Euler potentials, which represents the total energy per unit charge in the rotating frame, is specified as an integral of motion. For an electron-proton plasma, the integrals for both components are combined to yield the energy integral of the plasma as a whole and the integrated Ohm's law, in the limit of vanishing mass ratio of an electron to a proton.Maxwell's equations are divided in two parts: i.e., the co-rotational and non-corotational parts. It is shown that the electromagnetic potentials for these parts are derived from a scalar super-potential and a vector super-potential, respectively. 相似文献
20.
Non-linear hydrodynamical evolution of rotating relativistic stars: numerical methods and code tests
José A. Font † Nikolaos Stergioulas † Kostas D. Kokkotas † 《Monthly notices of the Royal Astronomical Society》2000,313(4):678-688
We present numerical hydrodynamical evolutions of rapidly rotating relativistic stars, using an axisymmetric, non-linear relativistic hydrodynamics code. We use four different high-resolution shock-capturing (HRSC) finite-difference schemes (based on approximate Riemann solvers) and compare their accuracy in preserving uniformly rotating stationary initial configurations in long-term evolutions. Among these four schemes, we find that the third-order piecewise parabolic method scheme is superior in maintaining the initial rotation law in long-term evolutions, especially near the surface of the star. It is further shown that HRSC schemes are suitable for the evolution of perturbed neutron stars and for the accurate identification (via Fourier transforms) of normal modes of oscillation. This is demonstrated for radial and quadrupolar pulsations in the non-rotating limit, where we find good agreement with frequencies obtained with a linear perturbation code. The code can be used for studying small-amplitude or non-linear pulsations of differentially rotating neutron stars, while our present results serve as testbed computations for three-dimensional general-relativistic evolution codes. 相似文献