共查询到20条相似文献，搜索用时 546 毫秒
1.
The paper deals with the study of a satellite attracted by n primary bodies, which form a relative equilibrium. We use orthogonal
degree to prove global bifurcation of planar and spatial periodic solutions from the equilibria of the satellite. In particular,
we analyze the restricted three body problem and the problem of a satellite attracted by the Maxwell’s ring relative equilibrium. 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.
4.
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
5.
James E. Howard 《Celestial Mechanics and Dynamical Astronomy》1990,48(3):267-288
The spectral stability of synchronous circular orbits in a rotating conservative force field is treated using a recently developed
Hamiltonian method. A complete set of necessary and sufficient conditions for spectral stability is derived in spherical geometry.
The resulting theory provides a general unified framework that encompasses a wide class of relative equilibria, including
the circular restricted three-body problem and synchronous satellite motion about an aspherical planet. In the latter case
we find an interesting class of stable nonequatorial circular orbits. A new and simplified treatment of the stability of the
Lagrange points is given for the restricted three-body problem. 相似文献
6.
We discuss existence and bifurcations of non-collinear (Lagrangian) relative equilibria in a generalized three body problem. Specifically, one of the bodies is a spheroid (oblate or prolate) with its equatorial plane coincident with the plane of motion where only the “J 2” term from its potential expansion is retained. We describe the bifurcations of relative equilibria as function of two parameters: J 2 and the angular velocity of the system formed by the mass centers. We offer the values of the parameters where bifurcations in shape occur and discuss their physical meaning. We conclude with a general theorem on the number and the shape of relative equilibria. 相似文献
7.
《New Astronomy》2024
We numerically study a version of the synchronous circular restricted three-body problem, where an infinitesimal mass body is moving under the Newtonian gravitational forces of two massive bodies. The primary body is an oblate spheroid while the secondary is an elongated asteroid of a combination of two equal masses forming a rotating dipole which is synchronous to the rotation of the primaries of the classic circular restricted three-body problem. In this paper, we systematically examine the existence, positions, and linear stability of the equilibrium points for various combinations of the model's parameters. We observe that the perturbing forces have significant effects on the positions and stability of the equilibrium points as well as the regions where the motion of the particle is allowed. The allowed regions of motion as determined by the zero-velocity surface and the corresponding isoenergetic curves as well as the positions of the equilibrium points are given. Finally, we numerically study the binary system Luhman-16 by computing the positions of the equilibria and their stability as well as the allowed regions of motion of the particle. The corresponding families of periodic orbits emanating from the collinear equilibrium points are computed along with their stability properties. 相似文献
8.
Effect of Moon perturbation on the energy curves and equilibrium points in the Sun–Earth–Moon system
《New Astronomy》2021
In this paper, we have considered that the Moon motion around the Earth is a source of a perturbation for the infinitesimal body motion in the Sun–Earth system. The perturbation effect is analyzed by using the Sun–Earth–Moon bi–circular model (BCM). We have determined the effect of this perturbation on the Lagrangian points and zero velocity curves. We have obtained the motion of infinitesimal body in the neighborhood of the equivalent equilibria of the triangular equilibrium points. Moreover, to know the nature of the trajectory, we have estimated the first order Lyapunov characteristic exponents of the trajectory emanating from the vicinity of the triangular equilibrium point in the proposed system. It is noticed that due to the generated perturbation by the Moon motion, the results are affected significantly, and the Jacobian constant is fluctuated periodically as the Moon is moving around the Earth. Finally, we emphasize that this model could be applicable to send either satellite or telescope for deep space exploration. 相似文献
9.
W. J. Robinson 《Celestial Mechanics and Dynamical Astronomy》1974,10(1):17-33
This paper is based on the restricted problem of three bodies with the unusual feature that the lightest particle is replaced by a rigid body. The attitude stability of the body is considered when its centre of mass is located at one of the equilibrium points. The stable attitude is determined when the satellite is stationary relative to the primaries. It is found that for some bodies there are two such attitudes, and these are determined. 相似文献
10.
The restricted 2+2 body problem is considered. The infinitesimal masses are replaced by triaxial rigid bodies and the equations of motion are derived in Lagrange form. Subsequently, the equilibrium solutions for the rotational and translational motion of the bodies are detected. These solutions are conveniently classified in groups according to the several combinations which are possible between the translational equilibria and the constant orientations of the bodies. 相似文献
11.
The equilibria and periodic orbits around a dumbbell-shaped body 总被引：1，自引：0，他引：1
This paper investigates the equilibria, their stability, and the periodic orbits in the vicinity of a rotating dumbbell-shaped body. First, the geometrical model of dumbbell-shaped body is established. The gravitational potential fields are obtained by the polyhedral method for several dumbbell-shaped bodies with various length–diameter ratios. Subsequently, the equilibrium points of these dumbbell-shaped bodies are computed and their stabilities are analyzed. Periodic orbits around equilibrium points are determined by the differential correction method. Finally, in order to understand further motion characteristic of dumbbell-shaped body, the effect of the rotating angular velocity of the dumbbell-shaped bodies is investigated. This study extends the research work of the orbital dynamics from simple shaped bodies to complex shaped bodies and the results can be applied to the dynamics of orbits around some asteroids. 相似文献
12.
R. F. Arenstorf 《Celestial Mechanics and Dynamical Astronomy》1978,17(4):331-355
Letn2 mass points with arbitrary masses move circularly on a rotating straight-line central-configuration; i.e. on a particular solution of relative equilibrium of then-body problem. Replacing one of the mass points by a close pair of mass points (with mass conservation) we show that the resultingN-body problem (N=n+1) has solutions, which are periodic in a rotating coordinate system and describe precessing nearlyelliptic motion of the binary and nearlycircular collinear motion of its center of mass and the other bodies; assuming that also the mass ratio of the binary is small. 相似文献
13.
K. Uldall Kristiansen M. Vereshchagin K. Goździewski P. L. Palmer R. M. Roberts 《Celestial Mechanics and Dynamical Astronomy》2012,112(2):169-190
In this paper we consider the two-body problem of a spherical pseudo-rigid body and a rigid sphere. Due to the rotational
and “re-labelling” symmetries, the system is shown to possess conservation of angular momentum and circulation. We follow
a reduction procedure similar to that undertaken in the study of the two-body problem of a rigid body and a sphere so that
the computed reduced non-canonical Hamiltonian takes a similar form. We then consider relative equilibria and show that the
notions of locally central and planar equilibria coincide. Finally, we show that Riemann’s theorem on pseudo-rigid bodies
has an extension to this system for planar relative equilibria. 相似文献
14.
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
15.
In this paper, the restricted problem of three bodies is generalized to include a case when the passively gravitating test particle is an oblate spheroid under effect of small perturbations in the Coriolis and centrifugal forces when the first primary is a source of radiation and the second one an oblate spheroid, coupled with the influence of the gravitational potential from the belt. The equilibrium points are found and it is seen that, in addition to the usual three collinear equilibrium points, there appear two new ones due to the potential from the belt and the mass ratio. Two triangular equilibrium points exist. These equilibria are affected by radiation of the first primary, small perturbation in the centrifugal force, oblateness of both the test particle and second primary and the effect arising from the mass of the belt. The linear stability of the equilibrium points is explored and the stability outcome of the collinear equilibrium points remains unstable. In the case of the triangular points, motion is stable with respect to some conditions which depend on the critical mass parameter; influenced by the small perturbations, radiating effect of the first primary, oblateness of the test body and second primary and the gravitational potential from the belt. The effects of each of the imposed free parameters are analyzed. The potential from the belt and small perturbation in the Coriolis force are stabilizing parameters while radiation, small perturbation in the centrifugal force and oblateness reduce the stable regions. The overall effect is that the region of stable motion increases under the combine action of these parameters. We have also found the frequencies of the long and short periodic motion around stable triangular points. Illustrative numerical exploration is rendered in the Sun–Jupiter and Sun–Earth systems where we show that in reality, for some values of the system parameters, the additional equilibrium points do not in general exist even when there is a belt to interact with. 相似文献
16.
The paper deals with a simple photo-gravitational model of N+1 bodies. The motion of a small particle which subjects both
the gravitational attraction and the radiation pressure is studied in a regular polygon configuration of N bodies. The dynamical
features of this model are investigated for a wide range of values of the radiation parameters by mapping its equilibrium
points and periodic orbits. The results show that for these values, radiation merely affects quantitatively the characteristics
of the system, while it leaves unaffected the stability of the particle periodic motions and equilibria.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
17.
David L. Richardson 《Celestial Mechanics and Dynamical Astronomy》1980,22(3):231-236
A lagrangian formulation for the three-dimensional motion of a satellite in the vicinity of the collinear points of the circular-restricted problem is reconsidered. It is shown that the influence of the primaries can be expressed in the form of two third-body disturbing functions. By use of this approach, the equations for the Lagrangian and for the motion itself are readily developed into highly compact expressions. All orders of the non-linear developments are shown to be easily obtainable using well-known recursive relationships. The resulting forms for these equations are well suited for use in the initial phase of canonical or non-canonical investigations. 相似文献
18.
Non-linear stability of the equilibria in the gravity field of a finite straight segment 总被引：1，自引：0，他引：1
Andrés Riaguas Antonio Elipe Teodoro López-Moratalla 《Celestial Mechanics and Dynamical Astronomy》2001,81(3):235-248
We study the non-linear stability of the equilibria corresponding to the motion of a particle orbiting around a finite straight segment. The potential is a logarithmic function and may be considered as an approximation to the one generated by elongated celestial bodies. By means of the Arnold's theorem for non-definite quadratic forms we determine the orbital stability of the equilibria, for all values of the parameter k of the problem, resonant cases included. 相似文献
19.
We deal with the study of the spatial restricted three-body problem in the case where the small particle is far from the primaries, that is, the so-called comet case. We consider the circular problem, apply double averaging and compute the relative equilibria of the reduced system. It appears that, in the circular problem, we find not only part of the equilibria existing in the elliptic case, but also new ones. These critical points are in correspondence with periodic and quasiperiodic orbits and invariant tori of the non-averaged Hamiltonian. We explain carefully the transition between the circular and the elliptic problems. Moreover, from the relative equilibria of elliptic type, we obtain invariant 3-tori of the original system. 相似文献
20.
Stability of the planar full 2-body problem 总被引：1，自引：0，他引：1
D. J. Scheeres 《Celestial Mechanics and Dynamical Astronomy》2009,104(1-2):103-128
The stability of the Full Two-Body Problem is studied in the case where both bodies are non-spherical, but are restricted to planar motion. The mutual potential is expanded up to second order in the mass moments, yielding a highly symmetric yet non-trivial dynamical system. For this system we identify all relative equilibria and determine their stability properties, with an emphasis on finding the energetically stable relative equilibria and conditions for Hill stability of the system. The energetically stable relative equilibria always correspond to the classical “gravity gradient” configuration with the long ends of the two bodies pointed at each other, however there always exists a second equilibrium in this configuration at a closer separation that is unstable. For our model system we precisely map out the relations between these different configurations at a given value of angular momentum. This analysis identifies the fundamental physical constraints and limitations that exist on such systems, and has immediate applications to the stability of asteroid systems that are fissioned due to a rapid spin rate. Specifically, we find that all contact binary asteroids which are spun to fission will initially lie in an unstable dynamical state and can always re-impact. If the total system energy is positive, the fissioned system can disrupt directly from this relative equilibrium, while if it is negative the system is bound together. 相似文献