共查询到20条相似文献，搜索用时 500 毫秒
1.
2.
José Edmundo Mansilla 《Celestial Mechanics and Dynamical Astronomy》2006,94(3):249-269
Results are obtained about formal stability and instability of Hamiltonian systems with three degrees of freedom, two equal
frequencies and the matrix of the linear part is not diagonalizable, in terms of the coefficients of the development in Taylor
series of the Hamiltonian of the system. The results are applied to the study of stability of the Lagrangian solutions of
the Three Body-Problem in the case in which the center of mass is over the curve ρ*, on the border of the region of linear stability of Routh. The curve ρ* is divided symmetrically in three arcs in such a way that if the center of mass of the three particles lies on the central
arc, the Lagrangian solution is unstable in the sense of Liapunov (in finite order), while if the center of mass determines
one point that lies on one of the other two arcs of ρ*, then the Lagrangian solution is formally stable. 相似文献
3.
J. N. Tokis 《Astrophysics and Space Science》1975,36(2):427-438
The general equations of angular momentum and kinetic energy of a rotating deformable (or not rigid) body are discussed for a fixed and a rotating coordinate system. A new system of equations is developed for a deformable body of arbitrary form using the Lagrangian (vector) cisplacement up to the first order terms. The equations are, then, illustrated for a self-gravitating ceformable body perturbed by tides. 相似文献
4.
In the present paper, the motion of three rigid bodies is considered. With a set of new variables, and the 10 first integrals of the motion, the problem is reduced to a system of order 25 and one quadrature. The plane motions are characterized, and finally, an equation for the existence of central configurations (in particular, Lagrangian and Eulerian solutions) has been found. Besides, the case of three axisymmetric ellipsoids is studied. 相似文献
5.
H.-J. Schmidt 《Astronomische Nachrichten》1985,306(2):67-70
For field equations of 4th order, follwing from a Lagrangian “Ricci scalar plus Weyl scalar”, it is shown (using methods of non-standard analysis) that in a neighbourhood of Minkowski space there do not exist regular static spherically symmetric solutions. With that (besides the known local expansions about r = o nad r = ∞ resp.) for the first time a global statement on the existence of such solutions is given. Finally, this result will be discussed in connection with Einstein's particle programme. 相似文献
6.
An explicit Lagrangian for a system of charged particles to higher-order terms: Quadrupole radiation
Demetrios D. Dionysiou 《Astrophysics and Space Science》1983,94(2):413-418
Using a new way we give an explicit formula for the Lagrangian for any number of charged particles interacting with each other up to the fifth-order terms, assuming that this system does not emit dipole radiation. Knowing the Lagrangian up to the fifth-order terms, we obtain the quadrupole radiation of our system in exact agreement with the classical electromagnetic theory. 相似文献
7.
D. S. Schmidt 《Celestial Mechanics and Dynamical Astronomy》1988,45(1-3):201-206
The Hamiltonian function of the restricted problem of three bodies near the triangular Lagrangian point is normalized through sixth order terms with the help of MACSYMA. The same calculations were done previously with an algebraic processor in order to establish the stability at a critical value of the mass ratio. 相似文献
8.
This paper focuses on some aspects of the motion of a small particle moving near the Lagrangian points of the Earth–Moon system.
The model for the motion of the particle is the so-called bicircular problem (BCP), that includes the effect of Earth and
Moon as in the spatial restricted three body problem (RTBP), plus the effect of the Sun as a periodic time-dependent perturbation
of the RTBP. Due to this periodic forcing coming from the Sun, the Lagrangian points are no longer equilibrium solutions for
the BCP. On the other hand, the BCP has three periodic orbits (with the same period as the forcing) that can be seen as the
dynamical equivalent of the Lagrangian points. In this work, we first discuss some numerical methods for the accurate computation
of quasi-periodic solutions, and then we apply them to the BCP to obtain families of 2-D tori in an extended neighbourhood
of the Lagrangian points. These families start on the three periodic orbits mentioned above and they are continued in the
vertical (z and ż) direction up to a high distance. These (Cantor) families can be seen as the continuation, into the BCP, of the Lyapunov
family of periodic orbits of the Lagrangian points that goes in the (z, ż) direction. These results are used in a forthcoming work [9] to find regions where trajectories remain confined for a
very long time. It is remarkable that these regions seem to persist in the real system.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
Pablo Fosalba & Enrique Gaztañaga 《Monthly notices of the Royal Astronomical Society》1998,301(2):503-523
We present a simple and intuitive approximation for solving the perturbation theory (PT) of small cosmic fluctuations. We consider only the spherically symmetric or monopole contribution to the PT integrals, which yields the exact result for tree-graphs (i.e. at leading order). We find that the non-linear evolution in Lagrangian space is then given by a simple local transformation over the initial conditions, although it is not local in Euler space. This transformation is found to be described by the spherical collapse (SC) dynamics, as it is the exact solution in the shearless (and therefore local) approximation in Lagrangian space. Taking advantage of this property, it is straightforward to derive the one-point cumulants, ξJ , for both the unsmoothed and smoothed density fields to arbitrary order in the perturbative regime. To leading-order this reproduces, and provides us with a simple explanation for, the exact results obtained by Bernardeau. We then show that the SC model leads to accurate estimates for the next corrective terms when compared with the results derived in the exact perturbation theory making use of the loop calculations. The agreement is within a few per cent for the hierarchical ratios S J = ξ J /ξ J −1 2 . We compare our analytic results with N -body simulations, which turn out to be in very good agreement up to scales where σ ≈ 1. A similar treatment is presented to estimate higher order corrections in the Zel'dovich approximation. These results represent a powerful and readily usable tool to produce analytical predictions that describe the gravitational clustering of large-scale structure in the weakly non-linear regime. 相似文献
10.
The main results of Whitham's averaged Lagrangian method for the treatment of linear wave-trains in a weakly inhomogeneous, moving medium are presented briefly. This method is then applied to an ideal, isotropic, one-fluid plasma which can be taken for the lowest order approximation for the interplanetary solar wind expansion. 相似文献
11.
The Lagrangian equilateral points of a planetary orbit are points of equilibrium that trail at 60°, ahead (L4) or behind (L5), the trajectory of a planet. Jupiter is the only major planet in our Solar system harbouring a known population of asteroids at those locations. Here we report the existence of orbits close to the Lagrangian points of Saturn, stable at time-scales comparable to the age of the Solar system. By scaling with respect to the Trojan population we have estimated the number of objects that would populate the regions, which gives a significant figure. Moreover, mutual physical collisions over the age of the Solar system would be very rare, so the evaporation rate of this swarm arising from mutual interactions would be very low. A population of asteroids not self-collisionally evolved after their formation stage would be the first to be observed in our planetary system. Our present estimations are based on the assumption that the capture efficiency at Saturn's equilateral points is comparable with the one corresponding to Jupiter, thus our figures may be taken as upper limits. In any case, observational constraints on their number would provide fundamental clues to our understanding of the history of the outer Solar system. If they existed, the surface properties and size distribution of those objects would represent unusually valuable fossil records of our early planetary system. 相似文献
12.
H. Fuchs 《Astronomische Nachrichten》1986,307(5):281-283
The equations of motion for test particles with internal structure are derived from a general Lagrange principle. The internal structure of the particles is described by sets of unspecified geometric objects, which transform homogeneously both under coordinate and under gauge transformations. Most of the Lagrangian approaches known in the literature are special cases of our general formalism. 相似文献
13.
The effect of the eccentricity of a planet’s orbit on the stability of the orbits of its satellites is studied. The model
used is the elliptic Hill case of the planar restricted three-body problem. The linear stability of all the known families
of periodic orbits of the problem is computed. No stable orbits are found, the majority of them possessing one or two pairs
of real eigenvalues of the monodromy matrix, while a part of a family with complex instability is found. Two families of periodic
orbits, bifurcating from the Lagrangian points L1, L2 of the corresponding circular case are found analytically. These orbits are very unstable and the determination of their
stability coefficients is not accurate, so we compute the largest Liapunov exponent in their vicinity. In all cases these
exponents are positive, indicating the existence of chaotic motions 相似文献
14.
Enrique Gaztañaga & Pablo Fosalba 《Monthly notices of the Royal Astronomical Society》1998,301(2):524-534
In Paper I of this series, we introduced the spherical collapse (SC) approximation in Lagrangian space as a way of estimating the cumulants ξ J of density fluctuations in cosmological perturbation theory (PT). Within this approximation, the dynamics is decoupled from the statistics of the initial conditions, so we are able to present here the cumulants for generic non-Gaussian initial conditions, which can be estimated to arbitrary order including the smoothing effects. The SC model turns out to recover the exact leading-order non-linear contributions up to terms involving non-local integrals of the J -point functions. We argue that for the hierarchical ratios S J , these non-local terms are subdominant and tend to compensate each other. The resulting predictions show a non-trivial time evolution that can be used to discriminate between models of structure formation. We compare these analytic results with non-Gaussian N -body simulations, which turn out to be in very good agreement up to scales where σ ≲ 1. 相似文献
15.
We construct a non-stationary form of the Lagrangian of a material point with a known integral of motion and given monoparametric
family of evolving orbits. An equation for non-stationary space symmetrical ‘potential’ function of such Lagrangian is given
and this stands for the analog of Szebehely's (1974) equation. As an application of the problem, an integrable equation from
celestial mechanics of variable mass with use of non-perturbed orbits of evolving type is constructed. On its basis adiabatic
invariants of non-stationary two-body problem containing a tangential force are found.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
16.
Run-Qian Huang Han-Feng Song Shao-Lan Bi National Astronomical Observatories/Yunnan Observatory Chinese Academy of Sciences Kunming Graduate University of Chinese Academy of Sciences Beijing 《中国天文和天体物理学报》2007,7(2):235-244
Three importantphysical processes occurringin contact binarysystems are studied. The first one is the effect of spin, orbital rotation and tide on the structure of the components, which includes also the effect of meridian circulation on the mixing of the chemical elements in the components. The second one is the mass and energy exchange between the components. To describe the energy exchange, a new approach is introduced based on the understanding that the exchange is due to the release of the potential, kinetic and thermal energy of the exchanged mass. The third is the loss of mass and angular momentum through the outer Lagrangian point. The rate of mass loss and the angular momentum carried away by the lost mass are discussed. To show the effects of these processes, we follow the evolution of a binary system consisting of a 12M and a 5M star with mass exchange between the components and mass loss via the outer Lagrangian point, both with and without considering the effects of rotation and tide. The result shows that the effect of rotation and tide advances the start of the semi-detached and the contact phases, and delays the end of the hydrogen-burning phase of the primary. Furthermore, it can change not only the occurrence of mass and angular momentum loss via the outer Lagrangian point, but also the contact or semi-contact status of the system. Thus, this effect can result in the special phenomenon of short-term variations occurring over a slow increase of the orbital period. The occurrence of mass and angular momentum loss via the outer Lagrangian point can affect the orbital period of the system significantly, but this process can be influenced, even suppressed out by the effect of rotation and tide. The mass and energy exchange occurs in the common envelope. The net result of the mass exchange process is a mass transfer from the primary to the secondary during the whole contact phase. 相似文献
17.
The problem is considered of the slow outflow of gas from a Close Binary System with subsequent formation of a shell or cloud of matter around the whole system. It appears that with a small change of velocity introduced to the most external parts of the gaseous ring around one of the components the gas particles can flow out from the binary system leaving it through the external Lagrangian point. This process can lead to the formation of a shell around the binary star. The change in kinetic energy of a gas particle corresponding to the perturbation in its motion leading to the escape through the adjacent external Lagrangian point can be smaller than 10% of the total kinetic energy of the considered particle for the case of a ring around a component with mass equal to or larger than the mass of the companion. 相似文献
18.
Victor Szebehely Arthur L. Whipple 《Celestial Mechanics and Dynamical Astronomy》1984,34(1-4):125-133
The restricted problem of three bodies is generalized to the restricted problem of 2+n bodies. Instead of one body of small mass and two primaries, the system is modified so that there are several gravitationally interacting bodies with small masses. Their motions are influenced by the primaries but they do not influence the motions of the primaries. Several variations of the classical problem are discussed. The separate Jacobian integrals of the minor bodies are lost but a conservative (time-independent) Hamiltonian of the system is obtained. For the case of two minor bodies, the five Lagrangian points of the classical problem are generalized and fourteen equilibrium solutions are established. The four linearly stable equilibrium solutions which are the generalizations of the triangular Lagrangian points are once again stable but only for considerably smaller values of the mass parameter of the primaries than in the classical problem. 相似文献
19.
K. E. papadakis 《Celestial Mechanics and Dynamical Astronomy》1998,72(4):235-244
The nonlinear stability zones of the triangular Lagrangian points are determined numerically and the effect of radiation of primaries is considered, in addition to the known effect of mass distribution, using the photogravitational restricted threebody problem model. It is found that radiation also has a considerable effect reducing the stability zones. In cases of resonances, these zones are reduced to negligible size for some parameter values within the linear stability regions. 相似文献
20.
R. Broucke 《Celestial Mechanics and Dynamical Astronomy》1978,18(3):207-222
In this article we study a form of equations of motion which is different from Lagrange's and Hamilton's equations: Pfaff's equations of motion. Pfaff's equations of motion were published in 1815 and are remarkably elegant as well as general, but still they are much less well known. Pfaff's equations can also be considered as the Euler-Lagrange equations derived from the linear Lagrangian rather than the usual Lagrangian which is quadratic in the velocity components. The article first treats the theory of changes of variables in Pfaff's equations and the connections with canonical equations as well as canonical transformations. Then the applications to the perturbed two-body problem are treated in detail. Finally, the Pfaffians are given in Hill variables and Scheifele variables. With these two sets of variables, the use of the true anomaly as independent variable is also considered. 相似文献