共查询到20条相似文献，搜索用时 31 毫秒
1.
Haruo Yoshida 《Celestial Mechanics and Dynamical Astronomy》1987,40(1):51-66
The straight-line collision solution in the anisotropic Kepler problem is extended to a periodic solution by means of Sundman's analytic continuation. It is shown that this collision periodic solution is always exponentially unstable. 相似文献
2.
The accelerated Kepler problem (AKP) is obtained by adding a constant acceleration to the classical two-body Kepler problem.
This setting models the dynamics of a jet-sustaining accretion disk and its content of forming planets as the disk loses linear
momentum through the asymmetric jet-counterjet system it powers. The dynamics of the accelerated Kepler problem is analyzed
using physical as well as parabolic coordinates. The latter naturally separate the problem’s Hamiltonian into two unidimensional
Hamiltonians. In particular, we identify the origin of the secular resonance in the AKP and determine analytically the radius
of stability boundary of initially circular orbits that are of particular interest to the problem of radial migration in binary
systems as well as to the truncation of accretion disks through stellar jet acceleration. 相似文献
3.
Kenneth R. Meyer 《Celestial Mechanics and Dynamical Astronomy》1981,23(1):69-81
This paper shows that there exist two families of periodic solutions of the restrictedN-body problem which are close to large circular orbits of the Kepler problem. These solutions are shown to be of general elliptic type and hence are stable. If the restricted problem admits a symmetry, then there are symmetric periodic solutions which are close to large elliptic orbits of the Kepler problem. 相似文献
4.
A two-point boundary value problem of the Kepler orbit similar to Lambert’s problem is proposed. The problem is to find a
Kepler orbit that will travel through the initial and final points in a specified flight time given the radial distances of
the two points and the flight-direction angle at the initial point. The Kepler orbits that meet the geometric constraints
are parameterized via the universal variable z introduced by Bate. The formula for flight time of the orbits is derived. The admissible interval of the universal variable
and the variation pattern of the flight time are explored intensively. A numerical iteration algorithm based on the analytical
results is presented to solve the problem. A large number of randomly generated examples are used to test the reliability
and efficiency of the algorithm. 相似文献
5.
Yu. S. Osipov 《Celestial Mechanics and Dynamical Astronomy》1977,16(2):191-208
The main result of this paper is a theorem on the trajectory equivalence of phase flows on isoenergetic surfaces with a positive energy level in the Kepler problem and perturbed kepler problem. The following two facts are crucial for proving it: firstly, an isomorphism of the phase flow on an isoenergetic surface in the Kepler problem and the geodesic flow in a constant curvature space. The isomorphism is studied in detail. In particular, all the integrals of the Kepler problem are obtained proceeding from the group-theory considerations. The second fact is a generalization of the theorem on structural stability of Anosov flows onto non-compact manifolds. 相似文献
6.
In this paper we present Runge-Kutta-Nyström (RKN) pairs of orders 4(3) and 6(4). We choose a test orbit from the Kepler problem to integrate for a specific tolerance. Then we train the free parameters of the above RKN4(3) and RKN6(4) families to perform optimally. For that we form a neural network approach and minimize its objective function using a differential evolution optimization technique. Finally we observe that the produced pairs outperform standard pairs from the literature for Pleiades orbits and Kepler problem over a wide range of eccentricities and tolerances. 相似文献
7.
8.
Pertti Lounesto 《Celestial Mechanics and Dynamical Astronomy》1978,17(3):207-213
The singularity of the Kepler motion can be eliminated by means of the spinor regularization. The extensive integrals of the Kepler motion form a Lie algebra with respect to the Poisson bracket operation. Mayer-Gürr has shown that in the caseH>0 the corresponding Lie group is the multiplicative group of all real 4×4 unimodular matrices SL(4,R). Kustaanheimo has posed the problem of the identification of the corresponding Lie groups in the elliptic and parabolic cases. We solve this problem here and use the opportunity to introduce the concept of the Clifford algebra which is needed in our solution. 相似文献
9.
Using the continuation method we prove that the circular and the elliptic symmetric periodic orbits of the planar rotating
Kepler problem can be continued into periodic orbits of the planar collision restricted 3-body problem. Additionally, we also
continue to this restricted problem the so called “comet orbits”.
An erratum to this article can be found at 相似文献
10.
Action-angle variables for the Levi-Civita regularized planar Kepler problem were introduced independently first by Chenciner and then by Deprit and Williams. The latter used explicitly the so-called Lissajous variables. When applied to the transformed Keplerian Hamiltonian, the Lissajous transformation encounters the difficulty of being defined in terms of the constant frequency parameter, whereas the Kepler problem transformed into a harmonic oscillator involves the frequency as a function of an energy-related canonical variable. A simple canonical transformation is proposed as a remedy for this inconvenience. The problem is circumvented by adding to the physical time a correcting term, which occurs to be a generalized Kepler’s equation. Unlike previous versions, the transformation is symplectic in the extended phase space and allows the treatment of time-dependent perturbations. The relation of the extended Lissajous–Levi-Civita variables to the classical Delaunay angles and actions is given, and it turns out to be a straightforward generalization of the results published by Deprit and Williams. 相似文献
11.
Alessandro Margheri Rafael Ortega Carlota Rebelo 《Celestial Mechanics and Dynamical Astronomy》2014,120(1):19-38
We study the dynamics of Kepler problem with linear drag. We prove that motions with nonzero angular momentum have no collisions and travel from infinity to the singularity. In the process, the energy takes all real values and the angular velocity becomes unbounded. We also prove that there are two types of linear motions: capture–collision and ejection–collision. The behaviour of solutions at collisions is the same as in the conservative case. Proofs are obtained using the geometric theory of ordinary differential equations and two regularizations for the singularity of Kepler problem equation. The first, already considered in Diacu (Celest Mech Dyn Astron 75:1–15, 1999), is mainly used for the study of the linear motions. The second, the well known Levi-Civita transformation, allows to complete the study of the asymptotic values of the energy and to prove the existence of collision solutions with arbitrary energy. 相似文献
12.
Maria Dina Vivarelli 《Celestial Mechanics and Dynamical Astronomy》1985,36(4):349-364
In a previous note we have shown that the KS-transformation, introduced by Kustaanheimo and Stiefel into Celestial Mechanics for the regularization of the Kepler problem, may be formulated in terms of hypercomplex numbers as the product of a quaternion and its anti-involute, thus representing a particular morphism of the real algebra of quaternions-having for image the physical configuration space of the Kepler problem. In the present note we show, first, that this formulation allows a straight derivation of the Hopf fibering of the sphere S3 (characterized by unit quaternions) having the base space given by the sphere S2 (characterized by unit vectors), and secondly that the KS-transformation allows the quantization of the symplectic manifold S2 in the sense of Souriau, the associated quantum manifold S3 having a contact structure given by the bilinear relation characteristic of the KS-theory. Furthermore, after presenting a natural extension of the hypercomplex KS-transformation to the full phase space of the Kepler problem, we show that this extension allows the quantization of the manifold of Kepler orbits of fixed negative energy (manifold diffeomorphic to the symplectic product S2×S2). The energy levels satisfy a well known quantum integrality condition and the associated quantum manifold is diffeomorphic to the product manifold S3×S3 quotiented by a suitable equivalence relation.Research supported by the Consiglio Nazionale delle Ricerche of Italy, Gruppo per la Fisica-Matematica. 相似文献
13.
Maria Dina Vivarelli 《Celestial Mechanics and Dynamical Astronomy》1987,41(1-4):359-370
As an outcome of our previous notes [13, 14] on the quaternion regularization of the classical Kepler problem and pre-quantization of the Kepler manifold we show, first, that both the cross product of two quaternions and the cross product of their anti-involutes are susceptible of a simple geometrical representation in the ordinary 3-dimensional euclidean spaceR
3 and, secondly, that they satisfy anSO(4)-invariant relation that implies projection of curves from the quaternion space onto the spaceR
3. ThisSO(4)-invariance allows—in the particular case of orthogonal quaternions of equal norm—a straight derivation: (i) of the correspondence between the free motion on the surface of a sphereS
3 and the physical elliptical Kepler motion (collisions included) on a plane denoted by
w
; (ii) of the celebrated Kepler equation and (iii) of the Levi-Civita regularizing time transformation. With (i) and (ii) we recover some of Györgyi's [3] results. The aforesaid orbital plane
w
and the orbital plane *, arrived at independently by exploiting the Kustaanheimo-Stiefel regularizing transformation, are shown to be inclined exactly at an angle characterizing the ratio of the semi-axes of the elliptical orbits and intimately related to the cross product representation. Thus the eventual superimposition of the two planes confirms the intimate connection between the various regularization procedures—transforming the classical Kepler problem into the geodesic flow onS
3—and the Fock's procedure for the quantum theoretical Kepler problem of the hydrogen atom (accidental degeneracy).This research was supported by the Consiglio Nazionale delle Ricerche of Italy (C.N.R.-G.N.F.M.). 相似文献
14.
The planar isosceles three-body problem where the two symmetric bodies have small masses is considered as a perturbation of
the Kepler problem. We prove that the circular orbits can be continued to saddle orbits of the Isosceles problem. This continuation
is not possible in the elliptic case. Their perturbed orbits tend to a continued circular one or approach a triple collision.
The basic tool used is the study of the Poincaré maps associated with the periodic solutions.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
15.
Haley L. Gomez Loretta Dunne Stephen A. Eales Edward L. Gomez Michael G. Edmunds 《Monthly notices of the Royal Astronomical Society》2005,361(3):1012-1014
It has been suggested by Dwek that iron needles could explain the submillimetre emission from the Cas A supernova remnant (SNR) with only a very small total mass. We investigate whether a similar model holds for the Kepler SNR, and find that its emission could indeed be explained by a dust mass of less than 10−2 M⊙ , dependent on the axial ratio l / a of the needles – which we constrain to be less than 700. But the implied needle model for Kepler is inconsistent with that suggested for Cas A since either the needles would have to have a resistivity one or two orders of magnitude greater than those in Cas A or the electron density in Kepler's shocked plasma must be 40 times greater than suggested by X-ray observations. An additional problem with the needle model is that the implied thickness of the needles seems to be implausibly small, if the emission properties are calculated under the usual approximations. 相似文献
16.
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
17.
18.
The Kepler problem for the resistive force r/r
2 is known to have a conserved vector which is the analogue to Hamilton's vector for the standar Kepler problem. In this note it is shown in a very elementary way that many similar force laws display the same property. The orbit equation can be obtained easily in such cases. 相似文献
19.
The equations of motion of the planar three-body problem split into two parts, called an external part and an internal part. When the third mass approaches zero, the first part tends to the equations of the Kepler motion of the primaries and the second part to the equations of motion of the restricted problem.We discuss the Hill stability from these equations of motion and the energy integral. In particular, the Jacobi integral for the circular restricted problem is seen as an infinitesimal-mass-order term of the Sundman function in this context. 相似文献
20.
John G. Bryant 《Celestial Mechanics and Dynamical Astronomy》1999,73(1-4):269-280
We introduce a new kind of canonical variables that prove very useful when the order of a Hamiltonian system can be reduced
by one, as in the case of isoenergetic reduction, and of what we call homogeneous reduction. The Kepler Problem, Geometrical
Optics and McGehee Blow-up are discussed as examples. Finally we carry out the isoenergetic reduction of the general N-Body
Problem using the new variables, and briefly discuss its application to the problem of collision.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献