共查询到20条相似文献，搜索用时 453 毫秒
1.
Nadia A. Saad 《Astrophysics and Space Science》2003,284(3):1001-1012
The stellar problem of three bodies is studied. A Lie transform is used to eliminate the short and intermediate periodic terms
from Harrington's Hamiltonian. The resulting system is a one of two degrees of freedom whose further reduction requires recourse
to numerical procedures.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
2.
We consider the non-canonical Hamiltonian dynamics of a gyrostat in Newtonian interaction with n spherical rigid bodies. Using the symmetries of the system we carry out two reductions. Then, working in the reduced problem,
we obtain the equations of motion, a Casimir function of the system and the equations that determine the relative equilibria.
Global conditions for existence of relative equilibria are given. Besides, we give the variational characterization of these
equilibria and three invariant manifolds of the problem; being calculated the equations of motion in these manifolds, which
are described by means of a canonical Hamiltonian system. We give some Eulerian and Lagrangian equilibria for the four body
problem with a gyrostat. Finally, certain classical problems of Celestial Mechanics are generalized. 相似文献
3.
V. Szebehely 《Celestial Mechanics and Dynamical Astronomy》1977,15(1):107-110
An analytical stability eriterion is given by the limiting value of the ratio of the semi-major axes of the outer star and inner binary and Harrington's (1972) numerically obtained results are slightly modified for planar systems in direct motion. 相似文献
4.
We consider a restricted charged four body problem which reduces to a two degrees of freedom Hamiltonian system, and prove the existence of infinite symmetric periodic orbits with arbitrarily large extremal period. Also, it is shown that an appropriate restriction of a Poincaré map of the system is conjugate to the shift homeomorphism on a certain symbolic alphabet.Partially supported by a grant of the CGICT no. P1386-0351.On leave of absence from Departamento de Fisica, Universidade de Lisboa. Partially supported by a grant of Fundaçao Calouste Gulbenkian no. 32/85/13. 相似文献
5.
For a Hamiltonian that can be separated into N+1(N\geq 2) integrable parts, four algorithms can be built for a symplectic integrator. This research compares these algorithms for the
first and second order integrators. We found that they have similar local truncation errors represented by error Hamiltonian
but rather different numerical stability. When the computation of the main part of the Hamiltonian, H
0, is not expensive, we recommend to use S
* type algorithm, which cuts the calculation of the H
0 system into several small time steps as Malhotra(1991) did. As to the order of the N+1 parts in one step calculation, we found that from the large to small would get a slower error accumulation.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
6.
Cezary Migaszewski Krzysztof Go&#;dziewski 《Monthly notices of the Royal Astronomical Society》2008,388(2):789-802
We present the secular theory of coplanar N -planet system, in the absence of mean motion resonances between the planets. This theory relies on the averaging of a perturbation to the two-body problem over the mean longitudes. We expand the perturbing Hamiltonian in Taylor series with respect to the ratios of semimajor axes which are considered as small parameters, without direct restrictions on the eccentricities. Next, we average out the resulting series term by term. This is possible thanks to a particular but in fact quite elementary choice of the integration variables. It makes it possible to avoid Fourier expansions of the perturbing Hamiltonian. We derive high-order expansions of the averaged secular Hamiltonian (here, up to the order of 24) with respect to the semimajor axes ratio. The resulting secular theory is a generalization of the octupole theory. The analytical results are compared with the results of numerical (i.e. practically exact) averaging. We estimate the convergence radius of the derived expansions, and we propose a further improvement of the algorithm. As a particular application of the method, we consider the secular dynamics of three-planet coplanar system. We focus on stationary solutions in the HD 37124 planetary system. 相似文献
7.
8.
Bin Kang Cheng 《Celestial Mechanics and Dynamical Astronomy》1979,19(1):31-41
In this paper the first variational equations of motion about the triangular points in the elliptic restricted problem are investigated by the perturbation theories of Hori and Deprit, which are based on Lie transforms, and by taking the mean equations used by Grebenikov as our upperturbed Hamiltonian system instead of the first variational equations in the circular restricted problem. We are able to remove the explicit dependence of transformed Hamiltonian on the true anomaly by a canonical transformation. The general solution of the equations of motion which are derived from the transformed Hamiltonian including all the constant terms of any order in eccentricity and up to the periodic terms of second order in eccentricity of the primaries is given. 相似文献
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11.
A systematic method is presented to construct a mapping model for a near-conservative system, based on that of Hadjidemetriou for a Hamiltonian system [1]. The mapping we constructed preserves the basic features of the actual system. We apply this method to the forced oscillating system and to the 3 : 1 resonant grain motion in the presence of Poynting-Robertson drag.Supported by the National Natural Science Foundation of China. 相似文献
12.
Efi Meletlidou 《Celestial Mechanics and Dynamical Astronomy》2000,78(1-4):161-166
We consider a one-dimensional non-degenerate Hamiltonian system perturbed by a periodically time dependent non-Hamiltonian vector field and show that the non-vanishing of the Melnikov subharmonic function is strongly related to the non-existence of an analytic integral in the perturbed system. 相似文献
13.
The spatial restricted rhomboidal five-body problem, or shortly, SRRFBP, is a five body problem in which four positive masses, called the primaries, move two by two in coplanar circular motions with the center of mass fixed at the origin such that their configuration is always a rhombus, the fifth mass being negligible and not influencing the motion of the four primaries. The Hamiltonian function that governs the motion of the fifth mass is derived and has three degrees of freedom depending periodically on time. Using a synodical system of coordinates, we fix the primaries in order to eliminate the time dependence. With the help of the Hamiltonian structure, we characterize the regions of possible motion. The vertical $z$ axis is invariant and we study what we call the rhomboidal Sitnikov problem. Unlike the classical Sitnikov problem, no chaos exists and the behavior of the fifth mass is quite predictable, periodic solutions of arbitrary long periods are shown to exist and we study numerically their linear horizontal stability. 相似文献
14.
The extension of the adiabatic invariant theory for one-degree of freedom Hamiltonian systems with varying parameters proposes a way of evaluating the probability of capture from one domain of the phase space into another. We derive here analytic expressions for these probabilities for a typical model of resonance of orderN. We show that the probabilities depend only upon two parameters and not four as expected a priori. 相似文献
15.
Giuseppe Pucacco 《New Astronomy》2012,17(5):475-482
We compute the normal forms for the Hamiltonian leading to the epicyclic approximations of the (perturbed) Kepler problem in the plane. The Hamiltonian setting corresponds to the dynamics in the Hill synodic system where, by means of the tidal expansion of the potential, the equations of motion take the form of perturbed harmonic oscillators in a rotating frame. In the unperturbed, purely Keplerian case, the post-epicyclic solutions produced with the normal form coincide with those obtained from the expansion of the solution of the Kepler equation. In all cases where the perturbed problem can be cast in autonomous form, the solution is easily obtained as a perturbation series. The generalization to the spatial problem and/or the non-autonomous case is straightforward. 相似文献
16.
J. F. Palacián 《Celestial Mechanics and Dynamical Astronomy》2007,98(4):219-249
We study the dynamics of a satellite (artificial or natural) orbiting an Earth-like planet at low altitude from an analytical
point of view. The perturbation considered takes into account the gravity attraction of the planet and in particular it is
caused by its inhomogeneous potential. We begin by truncating the equations of motion at second order, that is, incorporating
the zonal and the tesseral harmonics up to order two. The system is formulated as an autonomous Hamiltonian and has three
degrees of freedom. After three successive Lie transformations, the system is normalised with respect to two angular co-ordinates
up to order five in a suitable small parameter given by the quotient between the angular velocity of the planet and the mean
motion of the satellite. Our treatment is free of power expansions of the eccentricity and of truncated Fourier series in
the anomalies. Once these transformations are performed, the truncated Hamiltonian defines a system of one degree of freedom
which is rewritten as a function of two variables which generate a phase space which takes into account all of the symmetries
of the problem. Next an analysis of the system is achieved obtaining up to six relative equilibria and three types of bifurcations.
The connection with the original system is established concluding the existence of various families of invariant 3-tori of
it, as well as quasiperiodic and periodic trajectories. This is achieved by using KAM theory techniques. 相似文献
17.
In this paper the problem of two, and thus, after a generalization, of an arbitrary finite number, of rigid bodies is considered. We show that the Newton-Euler equations of motion are Hamiltonian with respect to a certain non-canonical structure. The system possesses natural symmetries. Using them we shown how to perform reduction of the number of degrees of freedom. We prove that on every stage of this process equations of motion are Hamiltonian and we give explicite form corresponding of non-canonical Poisson bracket. We also discuss practical consequences of the reduction. We prove the existence of 36 non-Lagrangean relative equilibria for two generic rigid bodies. Finally, we demonstrate that our approach allows to simplify the general form of the mutual potential of two rigid bodies. 相似文献
18.
The averaging theory of first order is applied to study a generalization of the Friedmann–Robertson–Walker Hamiltonian systems with three parameters. We provide sufficient conditions on the three parameters of the generalized system to guarantee the existence of continuous families of periodic orbits parameterized by the energy, and these families are given up to first order in a small parameter. 相似文献
19.
Haruo Yoshida 《Celestial Mechanics and Dynamical Astronomy》2002,83(1-4):355-364
Symplectic integration methods conserve the Hamiltonian quite well because of the existence of the modified Hamiltonian as a formal conserved quantity. For a first integral of a given Hamiltonian system, the modified first integral is defined to be a formal first integral for the modified Hamiltonian. It is shown that the Runge-Lenz vector of the Kepler problem is not well conserved by symplectic methods, and that the corresponding modified first integral does not exist. This conclusion is given for a one-parameter family of symplectic methods including the symplectic Euler method and the Störmer/Verlet method. 相似文献
20.
The problem of two gyrostats in a central force field is considered. We prove that the Newton-Euler equations of motion are
Hamiltonian with respect to a certain non-canonical structure. The system posseses symmetries. Using them we perform the reduction
of the number of degrees of freedom. We show that at every stage of the reduction process, equations of motion are Hamiltonian
and give explicit forms corresponding to non-canonical Poisson brackets. Finally, we study the case where one of the gyrostats
has null gyrostatic momentum and we study the zero and the second order approximation, showing that all equilibria are unstable
in the zero order approximation.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献