共查询到20条相似文献，搜索用时 62 毫秒
1.
Radu Balan 《Celestial Mechanics and Dynamical Astronomy》1995,63(1):59-79
The purpose of this paper is to study the motion of a spinless axisymmetric rigid body in a Newtonian field when we suppose the motion of the center of mass of the rigid body is on a Keplerian orbit. In this case the system can be reduced to a Hamiltonian system with configuration space of a two-dimensional sphere. We prove that the restricted planar motion is analytical nonintegrable and we find horseshoes due to the eccentricity of the orbit. In the caseI
3/I
1>4/3, we prove that the system on the sphere is also analytical nonintegrable.On leave from the Polytechnic Institute of Bucharest, Romania. 相似文献
2.
T. G. Vozmischeva 《Celestial Mechanics and Dynamical Astronomy》2002,84(1):65-85
The generalization of the two-center problem and the Lagrange problem (a mass point motion under the action of attracting center field and the analog of a constant homogeneous field) to the case of a constant curvature space, in the three-dimensional space of Lobachevsky (3), is investigated in this paper. The integrability of these problems is proved. The bifurcation set in the plane of integrals of motion is constructed and the classification of the domains of possible motion is carried out. An analog of a constant homogeneous field is obtained in the Lobachevsky space. 相似文献
3.
The Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids has been investigated in the presence of a two-dimensional horizontal uniform magnetic field. The streaming motion is also assumed to be two-dimensional. The stability analysis has been carried out for two highly viscous fluids of uniform densities. It is found that the streaming motion has dual influence on the unstable system, destabilizing for low values of streaming velocity and stabilizing for high values of streaming velocity. The effect of viscosity is, however, found to be stabilizing as the growth rate of the unstable configuration decreases on increasing the viscosity. 相似文献
4.
V. I. Ferronsky S. A. Denisik S. V. Ferronsky 《Celestial Mechanics and Dynamical Astronomy》1996,64(3):167-183
The physical meaning of the terms of the potential and kinetic energy expressions, expanded by means of the density variation function for a nonuniform self-gravitating sphere, is discussed. The terms of the expansions represent the energy and the moment of inertia of the uniform sphere, the energy and the moment of inertia of the nonuniformities interacting with the uniform sphere, and the energy of the nonuniformities interacting with each other. It follows from the physical meaning of the above components of the energy structure, and also from the observational fact of the expansion of the Universe that the phase transition, notably, fusion of particles and nuclei and condensation of liquid and solid phases of the expanded matter accompanied by release of energy, must be the physical cause of initial thermal and gravitational instability of the matter. The released kinetic energy being constrained by the general motion of the expansion, develops regional and local turbulent (cyclonic) motion of the matter, which should be the second physical effect responsible for the creation of celestial bodies and their rotation. 相似文献
5.
Despina Voyatzi Simos Ichtiaroglou 《Celestial Mechanics and Dynamical Astronomy》2005,93(1-4):331-342
We study the problem of the motion of a unit mass on the unit sphere
and examine the relation between integrability and certain monoparametric families of orbits. In particular we show that
if the potential is compatible with a family of meridians, it is integrable with an integral linear in the velocities, while
a family of parallels guarantees integrability with an integral quadratic in the velocities. 相似文献
6.
V. G. Demin Y. G. Markov I. S. Minyaev 《Celestial Mechanics and Dynamical Astronomy》1990,50(3):231-249
In the restricted three-body problem we consider the motion of a viscously elastic sphere (planet) with its centre of mass moving in a conditionally-periodic orbit. The approximate equations describing the rotational motion of the sphere in terms of the Andoyer variables are obtained by the method of the separation of motion and averaging; the evolution of the motion is also analysed. 相似文献
7.
We study Harrington's Hamiltonian in the Hill approximation of the stellar problem of three bodies in order to clarify and sharpen a qualitative analysis made by Lidov and Ziglin. We show how the orbital space after four reductions is a two-dimensional sphere, Harrington's Hamiltonian defining a biparametric dynamical system. We produce the diagrams corresponding to each type of phase flow according to a complete discussion of all possible local and global bifurcations determined by the four integrals of the system. 相似文献
8.
Sergei M. Poleshchikov 《Celestial Mechanics and Dynamical Astronomy》2003,85(4):341-393
The sets of L-matrices of the second, fourth and eighth orders are constructed axiomatically. The defining relations are taken from the regularization of motion equations for Keplerian problem. In particular, the Levi-Civita matrix and KS-matrix are L-matrices of second and fourth order, respectively. A theorem on the ranks of L-transformations of different orders is proved. The notion of L-similarity transformation is introduced, certain sets of L-matrices are constructed, and their classification is given. An application of fourth order L-matrices for N-body problem regularization is given. A method of correction for regular coordinates in the Runge–Kutta–Fehlberg integration method for regular motion equations of a perturbed two-body problem is suggested. Comparison is given for the results of numerical integration in the problem of defining the orbit of a satellite, with and without the above correction method. The comparison is carried out with respect to the number of calls to the subroutine evaluating the perturbational accelerations vector. The results of integration using the correction turn out to be in a favorable position. 相似文献
9.
Anne-Sophie Libert Jacques Henrard 《Celestial Mechanics and Dynamical Astronomy》2005,93(1-4):187-200
We analyse the secular interactions of two coplanar planets which are not in mean motion resonances. The analysis is based
on a high order (order 12) expansion of the perturbative potential in powers of the eccentricities. The model depends on only
two parameters (the ratio of semi-major axis and the mass ratio of the planets) and can be reduced to a one degree of freedom
system, allowing for an exhaustive parametric analysis. Following Pauwels [Pauwels T.: 1983, Celet. Mech. & Dyn. Astro. 30, 229–247] we map the phase space on a sphere, avoiding in this way the artificial singularities introduced by other mappings.
We show that the 12 order expansion is able to describe correctly most of the exosolar planetary systems discovered so far,
even if the eccentricities of these planets are considerably larger than the eccentricities of our own solar system. The expansion
is even able to reproduce, at moderate eccentricities, the secular resonances discovered numerically by Michtchenko and Malhotra
[Michtchenko, T. A. and Malhotra, R.: 2004, Icarus 168, 237–248] at moderate to large eccentricities.
FNRS Research Fellow. 相似文献
10.
Harry Dankowicz 《Celestial Mechanics and Dynamical Astronomy》1994,58(4):353-370
The motion has been studied of a particle in a gravitational field perturbed by radiation pressure. By combining the formulation in the physical space variables with the KS variables we obtained explicit evidence for the existence of a surface of stable circular orbits with centers on an axis through the primary body. Furthermore, the effects of a sharp shadow on the two-dimensional unstable parabolic orbits were investigated. It was found that they do not survive the introduction of a shadow. 相似文献
11.
Explosions of the electrolyzed ice envelopes of the Galilean satellites resulted in the appearance of a large number of ice fragments deep inside Jupiter's sphere of action. Gravitational perturbations by the Galilean satellites transferred these fragments from satellite orbits into the periphery of the sphere of action and beyond it. The fragments move initially in the direction of a satellite's motion tangentially to its orbit.The fragments have a small angular momentum since they come from deep inside Jupiter's sphere of action. On reaching the periphery of the sphere, the fragments can acquire retrograde motion (even in the sidereal frame) because of the Sun's action.If ejected from the zone of the Galilean satellites with a sufficient velocity, the fragments can leave Jupiter's sphere of action going both inside and outside its orbit, which leads to a substantial difference in the pattern of their subsequent motion in the vicinity of Jupiter's orbit.The results obtained may be used to shed light on the origin of the irregular satellites (Paper 1) and Trojans (Paper 2). 相似文献
12.
A coordinate system is defined on the phase space of a perturbed Keplerian system after the mean anomaly has been averaged out, for the purpose of explaining how eliminating the longitude of the ascending node reduces the orbital space to a two-dimensional sphere in case the system admits an axial symmetry. Concomitantly, on the submanifold of direct osculating ellipses, the CDM variables are replaced by functions which form the basis of a Poisson algebra isomorphic to the Lie algebra so(3) of the rotation group SO(3); furthermore, in these variables, the doubly reduced phase flow appears like a rotation of the reduced phase space. 相似文献
13.
N. Yu. Emel’yanenko 《Solar System Research》2012,46(3):181-194
This paper studies the dynamical evolution of 97 Jupiter-family comets over an 800-year time period. More than two hundred encounters with Jupiter are investigated, with the observed comets moving during a certain period of time in an elliptic jovicentric orbit. In most cases this is an ordinary temporary satellite capture of a comet in Everhart??s sense, not associated with a transition of the small body into Jupiter??s family of satellites. The phenomenon occurs outside the Hill sphere with comets with a high Tisserand constant relative to Jupiter; the comets?? orbits have a small inclination to the ecliptic plane. An analysis of 236 encounters has allowed the determination within the planar pair two-body problem of a region of orbits in the plane (a, e) whose semimajor axes and eccentricities contribute to the phenomenon under study. Comets with orbits belonging to this region experience a temporary satellite capture during some of their encounters; the jovicentric distance function has several minima; and the encounters are characterized by reversions of the line of apsides and some others features of their combination that are intrinsic to comets in this region. Therefore, this region is called a region of comets with specific features in their encounters with Jupiter. Twenty encounters (out of 236), whereby the comet enters an elliptic jovicentric orbit in the Hill sphere, are identified and investigated. The size and shape of the elliptic heliocentric orbits enabling this transition are determined. It is found that in 11 encounters the motion of small bodies in the Hill sphere has features the most important of which is multiple minima of the jovicentric distance function. The study of these 20 encounters has allowed the introduction of the concept of temporary gravitational capture of a small body into the Hill sphere. An analysis of variations in the Tisserand constant in these (20) encounters of the observable comets shows that their motion is unstable in Hill??s sense. 相似文献
14.
We have two mass points of equal masses m
1=m
2 > 0 moving under Newton’s law of attraction in a non-collision parabolic orbit while their center of mass is at rest. We
consider a third mass point, of mass m
3=0, moving on the straight line L perpendicular to the plane of motion of the first two mass points and passing through their
center of mass. Since m
3=0, the motion of m
1 and m
2 is not affected by the third and from the symmetry of the motion it is clear that m
3 will remain on the line L. The parabolic restricted three-body problem describes the motion of m
3. Our main result is the characterization of the global flow of this problem. 相似文献
15.
Variations of the cosmic ray cut-off rigidities have been observed at mid latitudes during the magnetic storm period 16–18 December 1971. In the present paper the cut-off changes over Europe are determined on an hourly basis from the registrations of 10 European neutron monitor stations. As a first order approximation it is assumed that the observed cut-off variations originate from a spherical current sheet concentric with the Earth and with a current density proportional to the cosine of the geomagnetic latitude. Applying results obtained by Treiman (1953), the radii of the current sphere can then be deduced from the dependences of the relative cut-off rigidity variations on geomagnetic latitude. The sphere is found to be located between 4 and 6 Earth radii during the main phase of the magnetic storm on 17 December 1971. A comparison of these results with in situ measurements carried out in the equatorial plane by Explorer 45 shows good agreement. 相似文献
16.
17.
V. P. Tomanov 《Kinematics and Physics of Celestial Bodies》2007,23(5):196-206
We analyze our earlier data on the numerical integration of the equations of motion for 274 short-period comets (with the period P<200 yr) on a time interval of 6000 yr. As many as 54 comets had no close approaches to planets, 13 comets passed through the Saturnian sphere of action, and one comet passed through the Uranian sphere of action. The orbital elements of these 68 comets changed by no more than ±3 percent in a space of 6000 yr. As many as 206 comets passed close to Jupiter. We confirm Everhart’s conclusion that Jupiter can capture long-period comets with q = 4–6 AU and i < 9° into short-period orbits. We show that nearly parabolic comets cross the solar system mainly in the zone of terrestrial planets. No relationship of nearly parabolic comets and terrestrial planets was found for the epoch of the latest apparition of comets. Guliev’s conjecture about two trans-Plutonian planets is based on the illusory excess of cometary nodes at large heliocentric distances. The existence of cometary nodes at the solar system periphery turns out to be a solely geometrical effect. 相似文献
18.
V. S. Kalantonis E. A. Perdios A. E. Perdiou M. N. Vrahatis 《Celestial Mechanics and Dynamical Astronomy》2001,80(2):81-96
The accurate computation of families of periodic orbits is very important in the analysis of various celestial mechanics systems. The main difficulty for the computation of a family of periodic orbits of a given period is the determination within a given region of an individual member of this family which corresponds to a periodic orbit. To compute with certainty accurate individual members of a specific family we apply an efficient method using the Poincaré map on a surface of section of the considered problem. This method converges rapidly, within relatively large regions of the initial conditions. It is also independent of the local dynamics near periodic orbits which is especially useful in the case of conservative dynamical systems that possess many periodic orbits, often of the same period, close to each other in phase space. The only computable information required by this method is the signs of various function evaluations carried out during the integration of the equations of motion. This method can be applied to any system of celestial mechanics. In this contribution we apply it to the photogravitational problem. 相似文献
19.
Numerical orbit integrations have been conducted to characterize the types of trajectories in the one-dimensional Newtonian three-body problem with equal masses and positive energy. At positive energies the basic types of motions are binary + single particle and ionization, and when time goes from – to + all possible transitions between these states can take place. Properties of individual orbits have been summarized in the form of graphical maps in a two-dimensional grid of initial values. The basic motion types exist at all positive energies, but the binary + single particle configuration is obtained only in a narrow region of initial values if the total energy is large. At very large energies the equations of motion can be solved approximately, and this asymptotic result, exact in the limit of infinite energy, is presented. 相似文献
20.
P. G. Kazantzis 《Astrophysics and Space Science》1979,61(2):287-316
A systematic and detailed discussion of the gravitational spring-pendulum problem is given for the first time. A procedure is developed for the numerical treatment of non-integrable dynamical systems which possess certain properties in common with the gravitational problem. The technique is important because, in contrast to previous studies, it discloses completely the structure of two-dimensional periodic motion by examining the stability of the one-dimensional periodic motion. Through the parameters of this stability, points have been predicted from which the one-dimensional motion bifurcates into two-dimensional motion. Consequently, families of two-dimensional periodic solutions emanated from these points are studied. These families constitute the generators of the mesh of all the families of periodic solutions of the problem. 相似文献