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1.
Some properties of the dumbbell satellite attitude dynamics   总被引：1，自引：0，他引：1  
The dumbbell satellite is a simple structure consisting of two point masses connected by a massless rod. We assume that it moves around the planet whose gravity field is approximated by the field of the attracting center. The distance between the point masses is assumed to be much smaller than the distance between the satellite’s center of mass and the attracting center, so that we can neglect the influence of the attitude dynamics on the motion of the center of mass and treat it as an unperturbed Keplerian one. Our aim is to study the satellite’s attitude dynamics. When the center of mass moves on a circular orbit, one can find a stable relative equilibrium in which the satellite is permanently elongated along the line joining the center of mass with the attracting center (the so called local vertical). In case of elliptic orbits, there are no stable equilibrium positions even for small values of the eccentricity. However, planar periodic motions are determined, where the satellite oscillates around the local vertical in such a way that the point masses do not leave the orbital plane. We prove analytically that these planar periodic motions are unstable with respect to out-of-plane perturbations (a result known from numerical investigations cf. Beletsky and Levin Adv Astronaut Sci 83, 1993). We provide also both analytical and numerical evidences of the existence of stable spatial periodic motions.  相似文献   

2.
We investigate the stability of the periodic motion of a satellite, a rigid body, relative to the center of mass in a central Newtonian gravitational field in an elliptical orbit. The orbital eccentricity is assumed to be low. In a circular orbit, this periodic motion transforms into the well-known motion called hyperboloidal precession (the symmetry axis of the satellite occupies a fixed position in the plane perpendicular to the radius vector of the center of mass relative to the attractive center and describes a hyperboloidal surface in absolute space, with the satellite rotating around the symmetry axis at a constant angular velocity). We consider the case where the parameters of the problem are close to their values at which a multiple parametric resonance takes place (the frequencies of the small oscillations of the satellite’s symmetry axis are related by several second-order resonance relations). We have found the instability and stability regions in the first (linear) approximation at low eccentricities.  相似文献   

3.
This paper contains an analysis of the attitude stability of a spinning axisymmetric satellite whose mass center moves in any known planar periodic orbit of the restricted three-body problem while the spin axis remains normal to the orbit plane. A procedure based on Floquet theory is developed for constructing attitude instability charts, and examples of these are presented for two stable periodic orbits of the Earth-Moon system—one direct and one retrograde. The physical significance of these instability predictions is then explored by means of numerical integration of the full nonlinear equations of motion. Finally, an analysis based on averaging is performed, leading to approximate instability charts and indicating a possible connection between certain orbital-attitude resonance conditions and unstable attitude motions.  相似文献   

4.
This paper is devoted to the dynamics in a central gravity field of two point masses connected by a massless tether (the so called “spring–mass” model of tethered satellite systems). Only the motions with straight strained tether are studied, while the case of “slack” tether is not considered. It is assumed that the distance between the point masses is substantially smaller than the distance between the system’s center of mass and the field center. This assumption allows us to treat the motion of the center of mass as an unperturbed Keplerian one, so to focus our study on attitude dynamics. A particular attention is given to the family of planar periodic motions in which the center of mass moves on an elliptic orbit, and the point masses never leave the orbital plane. If the eccentricity tends to zero, the corresponding family admits as a limit case the relative equilibrium in which the tether is elongated along the line joining the center of mass with the field center. We study the bifurcations and the stability of these planar periodic motions with respect to in-plane and out-of-plane perturbations. Our results show that the stable motions take place if the eccentricity of the orbit is sufficiently small.  相似文献   

5.
Gravity-gradient perturbations of the attitude motion of a tumbling tri-axial satellite are investigated. The satellite center of mass is considered to be in an elliptical orbit about a spherical planet and to be tumbling at a frequency much greater than orbital rate. In determining the unperturbed (free) motion of the satellite, a canonical form for the solution of the torque-free motion of a rigid body is obtained. By casting the gravity-gradient perturbing torque in terms of a perturbing Hamiltonian, the long-term changes in the rotational motion are derived. In particular, far from resonance, there are no long-period changes in the magnitude of the rotational angular momentum and rotational energy, and the rotational angular momentum vector precesses abound the orbital angular momentum vector.At resonance, a low-order commensurability exists between the polhode frequency and tumbling frequency. Near resonance, there may be small long-period fluctuations in the rotational energy and angular momentum magnitude. Moreover, the precession of the rotational angular momentum vector about the orbital angular momentum vector now contains substantial long-period contributions superimposed on the non-resonant precession rate. By averaging certain long-period elliptic functions, the mean value near resonance for the precession of the rotational angular momentum vector is obtained in terms of initial conditions.  相似文献   

6.
As is well known, the orbital and rotational motions of a solid are coupled, and the integrals of energy and angular momentum (in a gravitational field with spherical symmetry) impose restrictions on them. We study the regions allowed to the motion in configurational space. It turns out that even in the crudest model (planar motion of a triple rod) the restrictions on the libration angle and the orbital radius of the center of mass are coupled, so that excessive ellipticity of the orbit excludes stabilization in the neighbourhood of the spoke equilibrium position by gravitational forces only.Chargé de Cours.  相似文献   

7.
The analysis of the Moon artificial satellite orbits stability and satellite system configuring are important issues of lunar orbital navigational system development. The article analyses the influence of different combinations of perturbations on Moon artificial satellite’s obits evolution. The method of Moon artificial satellite’s orbital evolution analysis is offered; general stability regions of Moon artificial satellite’s orbits are defined and the quality characteristics of the selected orbital groups of the satellite system are evaluated.  相似文献   

8.
Differential equations are derived for studying the effects of either conservative or nonconservative torques on the attitude motion of a tumbling triaxial rigid satellite. These equations, which are analogous to the Lagrange planetary equations for osculating elements, are then used to study the attitude motions of a rapidly spinning, triaxial, rigid satellite about its center of mass, which, in turn, is constrained to move in an elliptic orbit about an attracting point mass. The only torques considered are the gravity-gradient torques associated with an inverse-square field. The effects of oblateness of the central body on the orbit are included, in that, the apsidal line of the orbit is permitted to rotate at a constant rate while the orbital plane is permitted to precess (either posigrade or retrograde) at a constant rate with constant inclination.A method of averaging is used to obtain an intermediate set of averaged differential equations for the nonresonant, secular behavior of the osculating elements which describe the complete rotational motions of the body about its center of mass. The averaged differential equations are then integrated to obtain long-term secular solutions for the osculating elements. These solutions may be used to predict both the orientation of the body with respect to a nonrotating coordinate system and the motion of the rotational angular momentum about the center of mass. The complete development is valid to first order in (n/w 0)2, wheren is the satellite's orbital mean motion andw 0 its initial rotational angular speed.  相似文献   

9.
A research that we conducted in 1963 on the evolution of the binaries based on the available orbital data to obtain a philosophical degree, led to the establishment of an interesting and new diagram between the logarithm of the total mass and a particular parameterX, bound to the areal constant. This appeared to have a real physical significance but the basic observational material was insufficiently extended to assure its undeniable existence. In 1981, a new research based on a more extended orbital material, has confirmed this diagram. Presently, another important increase in the orbital material and the availability of highly accurate trigonometric parallaxes produced by the Hipparcos satellite, gave us the opportunity to confirm once more the stability of this diagram. This last research is here described.  相似文献   

10.
A method of general perturbations, based on the use of Lie series to generate approximate canonical transformations, is applied to study the effects of gravity-gradient torque on the rotational motion of a triaxial, rigid satellite. The center of mass of the satellite is constrained to move in an elliptic orbit about an attracting point mass. The orbit, which has a constant inclination, is free to precess and spin. The method of general perturbations is used to obtain the Hamiltonian for the nonresonant secular and long-period rotational motion of the satellite to second order inn/0, wheren is the orbital mean motion of the center of mass and0 is a reference value of the magnitude of the satellite's rotational angular velocity. The differential equations derivable from the transformed Hamiltonian are integrable and the solution for the long-term motion may be expressed in terms of Jacobian elliptic functions and elliptic integrals. Geometrical aspects of the long-term rotational motion are discussed and a comparison of theoretical results with observations is made.  相似文献   

11.
The faint E ring of Saturn appears as a narrow ring 246,000 ± 4,000 km from the center of Saturn on photographs taken when the ring-plane inclination was 5°.4. The apparent brightness of the ring was uniform at all observed orbital longitudes and permits an estimate of the normal optical thickness. A faint satellite (1981S1) was observed near the L4 triangular libration point of Tethys and is probably the same object as 1980S13.  相似文献   

12.
Long arc gravity analysis of lunar orbiter tracking data in the past has been carried out with the help of averaged equations of motion, in which short period effects have been suppressed. This procedure has required that the harmonic terms in the gravity potential be averaged over an orbital period. In the present paper, we extend this technique to mass points and mass discs in the gravity field. This required the evaluation of expressions for the mean rates of the orbit elements for a satellite perturbed by a lens shaped mass concentration. Corresponding expressions for the perturbations due to a mass point are obtained in the limit as the lens radius goes to zero. The derived equations have been programmed on the UNIVAC 1108 computer, and the results checked by numerical differencing.  相似文献   

13.
At the present state the rotational axes of Uranus and Pluto are nearly perpendicular to their orbital planes and each satellite moves in the vicinity of the equatorial plane of its mother planet. We assume that in the past a planet's equatorial plane was nearly coincident with its orbital plane and then the inclination of the equatorial plane with respect to the orbital plane began to increase secularly. Here we discuss whether a satellite that moves in its mother's equatorial plane continues to move in the equatorial plane or not. When the direct solar perturbation is neglected, the satellite continues to stay in the equatorial plane under the condition that the secular rate of change of the obliquity is slower than the precessional speed of the satellite orbital plane with respect to the equator.  相似文献   

14.
Attitude dynamics of a gravity oriented satellite in the presence of solar radiation pressure is examined. It is shown that even with a small offset between the satellite center of mass and center of pressure, significant pointing errors may result from the parametric excitation of the attitude motion by the radiation pressure. The phenomenon is illustrated through the analysis of a simple configuration involving a spherical shaped satellite possessing a nonspherical but axisymmetric mass distribution.  相似文献   

15.
The volume average of the strain tensor in a body moving in an inverse-square force field is evaluated. The calculation is carried out assuming the satellite to be an isotropic elastic body whose center of mass moves in a planar orbit. An approximate expression, in terms of its volume and elastic properties, is presented for the strain energy in the satellite. Using this expression the equation of planar librational motion is written explicity. This equation is discussed for both circular and elliptic orbits and is modified to include the effects of energy dissipation in the body. It is shown that the concept of Adiabatic Invariants allows one to analyze the influence of slow changes in the material volume and elasticity.This work was supported by NASA Grant No. NGR 05-010-020.  相似文献   

16.
Attitude motion of a satellite subjected to gravitational and aerodynamic torques in a circular orbit is investigated. In special case, when the center of pressure of aerodynamic forces is located on one of the principal central axes of inertia of the satellite, all equilibrium orientations are determined. Necessary and (or) sufficient conditions of stability are obtained for each equilibrium orientation. Evolution of domains where stability conditions take place is investigated. All bifurcation values of parameters corresponding to qualitative change of domains of stability are determined.  相似文献   

17.
The dynamics of the Kuiper Belt region between 33 and 63 au is investigated just taking into account the gravitational influence of Neptune. Indeed the aim is to analyse the information which can be drawn from the actual exoplanetary systems, where typically physical and orbital data of just one or two planets are available. Under this perspective we start our investigation using the simplest three-body model (with Sun and Neptune as primaries), adding at a later stage the eccentricity of Neptune and the inclinations of the orbital planes to evaluate their effects on the Kuiper Belt dynamics. Afterwards we remove the assumption that the orbit of Neptune is Keplerian by adding the effect of Uranus through the Lagrange–Laplace solution or through a suitable resonant normal form. Finally, different values of the mass ratios of the primary to the host star are considered in order to perform a preliminary analysis of the behaviour of exoplanetary systems. In all cases, the stability is investigated by means of classical tools borrowed from dynamical system theory, like Poincaré mappings and Lyapunov exponents.  相似文献   

18.
This paper studies libration dynamics and stability of deorbiting nano-satellites by short and bare electrodynamic tethers. A critical aspect of satellite deorbit by an electrodynamic tether is to maintain the tether aligned with the local vertical and stable while subjected to external perturbations. The dynamics of electrodynamic tether system in deorbit application is divided into the orbital motion of the center of system’s mass and the tether libration motion relative to that center. Major space environmental perturbations including the current-induced electrodynamic force, atmospheric drag, oblateness effect of the Earth, irregularity of geomagnetic field, variable plasma density, solar radiation pressure, and lunisolar gravitational attractions are considered in the dynamic analysis. Quantitative analyses are provided in order to characterize the order of the perturbative torques during the deorbit process. A single index is derived from the libration energy to stabilize the libration motion by regulating the current in the tether through simple on-off switching. Numerical results show that the libration dynamics of an electrodynamic tether has significant impacts on the deorbit process and the electrodynamic tether cannot effectively deorbit satellites without libration stability control. The proposed current regulation strategy is simple and very effective in stabilizing libration motion of an electrodynamic tether.  相似文献   

19.
The highly flattened distribution of satellite galaxies in the Milky Way (MW) presents a number of puzzles. First, its polar alignment stands out from the planar alignments commonly found in other galaxies. Secondly, recent proper-motion measurements reveal that the orbital angular momentum of at least three, and possibly as many as eight, of the MW's satellites points (within  30°  ) along the axis of their flattened configuration, suggesting some form of coherent motion. In this paper, we use a high-resolution cosmological simulation to investigate whether this pattern conflicts with the expectations of the cold dark matter model of structure formation. We find that this seemingly unlikely setup occurs often: approximately 35 per cent of the time, we find systems in which the angular momentum of three individual satellites points along, or close to, the short axis of the satellite distribution. In addition, in 30 per cent of the systems we find that the net angular momentum of the six best-aligned satellites lies within  35°  of the short axis of the satellite distribution, as observed for the MW.  相似文献   

20.
In this paper, we consider a satellite orbiting in a Manev gravitational potential under the influence of an atmospheric drag force that varies with the square of velocity. Using an exponential atmosphere that varies with the orbital altitude of the satellite, we examine a circular orbit scenario. In particular, we derive expressions for the change in satellite radial distance as a function of the drag force parameters and obtain numerical results. The Manev potential is an alternative to the Newtonian potential that has a wide variety of applications, in astronomy, astrophysics, space dynamics, classical physics, mechanics, and even atomic physics.  相似文献   

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