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1.
Hanlun Lei Christian Circi Emiliano Ortore Bo Xu 《Celestial Mechanics and Dynamical Astronomy》2018,130(8):53
In this work, periodic attitudes and bifurcations of periodic families are investigated for a rigid spacecraft moving on a stationary orbit around a uniformly rotating asteroid. Under the second degree and order gravity field of an asteroid, the dynamical model of attitude motion is formulated by truncating the integrals of inertia of the spacecraft at the second order. In this dynamical system, the equilibrium attitude has zero Euler angles. The linearised equations of attitude motion are utilised to study the stability of equilibrium attitude. It is found that there are three fundamental types of periodic attitude motions around a stable equilibrium attitude point. We explicitly present the linear solutions around a stable equilibrium attitude, which can be used to provide the initial guesses for computing the true periodic attitudes in the complete model. By means of a numerical approach, three fundamental families of periodic attitudes are studied, and their characteristic curves, distribution of eigenvalues, stability curves and stability distributions are determined. Interestingly, along the characteristic curves of the fundamental families, some critical points are found to exist, and these points correspond to tangent and period-doubling bifurcations. By means of a numerical approach, the bifurcated families of periodic attitudes are identified. The natural and bifurcated families constitute networks of periodic attitude families. 相似文献
2.
The aim of the present paper is to provide sufficient conditions for the existence of periodic solutions of the perturbed attitude dynamics of a rigid dumbbell satellite in a circular orbit. 相似文献
3.
Giacomo Giampieri 《Icarus》2004,167(1):228-230
A planetary body moving on an eccentric orbit around the primary is subject to a periodic perturbing potential, affecting its internal mass distribution. In a previous paper (Rappaport et al., 1997, Icarus 126, 313), we have calculated the periodic modulation of the gravity coefficients of degree 2, for a body on a synchronous orbit. Here, the previous analysis is extended by considering also non-synchronous orbits, and by properly accounting for the apparent motion of the primary due to the non uniform motion along the elliptical orbit. The cases of Titan and Mercury are briefly discussed. 相似文献
4.
The effect of the eccentricity of a planet’s orbit on the stability of the orbits of its satellites is studied. The model
used is the elliptic Hill case of the planar restricted three-body problem. The linear stability of all the known families
of periodic orbits of the problem is computed. No stable orbits are found, the majority of them possessing one or two pairs
of real eigenvalues of the monodromy matrix, while a part of a family with complex instability is found. Two families of periodic
orbits, bifurcating from the Lagrangian points L1, L2 of the corresponding circular case are found analytically. These orbits are very unstable and the determination of their
stability coefficients is not accurate, so we compute the largest Liapunov exponent in their vicinity. In all cases these
exponents are positive, indicating the existence of chaotic motions 相似文献
5.
Some properties of the dumbbell satellite attitude dynamics 总被引：1，自引：0，他引：1
Alessandra Celletti Vladislav Sidorenko 《Celestial Mechanics and Dynamical Astronomy》2008,101(1-2):105-126
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
6.
E. V. Polyachenko V. L. Polyachenko I. G. Shukhman 《Monthly notices of the Royal Astronomical Society》2007,379(2):573-596
We study spherical and disc clusters in a near-Keplerian potential of galactic centres or massive black holes. In such a potential orbit precession is commonly retrograde, that is, the direction of the orbit precession is opposite to the orbital motion. It is assumed that stellar systems consist of nearly-radial orbits. We show that if there is a loss-cone at low angular momentum (e.g. due to consumption of stars by a black hole), an instability similar to loss-cone instability in plasma may occur. The gravitational loss-cone instability is expected to enhance black hole feeding rates. For spherical systems, the instability is possible for the number of spherical harmonics l ≥ 3 . If there is some amount of counter-rotating stars in flattened systems, they generally exhibit the instability independent of azimuthal number m . The results are compared with those obtained recently by Tremaine for distribution functions monotonically increasing with angular momentum.
The analysis is based on simple characteristic equations describing small perturbations in a disc or a sphere of stellar orbits highly elongated in radius. These characteristic equations are derived from the linearized Vlasov equations (combining the collisionless Boltzmann kinetic equation and the Poisson equation), using the action-angle variables. We use two techniques for analysing the characteristic equations: the first one is based on preliminary finding of neutral modes, and the second one employs a counterpart of the plasma Penrose–Nyquist criterion for disc and spherical gravitational systems. 相似文献
The analysis is based on simple characteristic equations describing small perturbations in a disc or a sphere of stellar orbits highly elongated in radius. These characteristic equations are derived from the linearized Vlasov equations (combining the collisionless Boltzmann kinetic equation and the Poisson equation), using the action-angle variables. We use two techniques for analysing the characteristic equations: the first one is based on preliminary finding of neutral modes, and the second one employs a counterpart of the plasma Penrose–Nyquist criterion for disc and spherical gravitational systems. 相似文献
7.
Douglas C. Heggie 《Celestial Mechanics and Dynamical Astronomy》1985,35(4):357-382
In an autonomous Hamiltonian system with three or more degrees of freedom, a family of periodic orbits may become unstable when two pairs of characteristic multipliers coallesce on the unit circle at points not equal to ±1, and then move off the unit circle. This paper develops normal forms suitable for the neighbourhood of such an, instability, and, at this approximation, demonstrates the bifurcation from the periodic orbit of a family of invariant two-dimensional tori. The theory is illustrated with numerical computations of orbits of the planar general three-body problem. 相似文献
8.
Vladislav V. Sidorenko Alessandra Celletti 《Celestial Mechanics and Dynamical Astronomy》2010,107(1-2):209-231
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
9.
The importance of the stability characteristics of the planar elliptic restricted three-body problem is that they offer insight
about the general dynamical mechanisms causing instability in celestial mechanics. To analyze these concerns, elliptic–elliptic
and hyperbolic–elliptic resonance orbits (periodic solutions with lower period) are numerically discovered by use of Newton's
differential correction method. We find indications of stability for the elliptic–elliptic resonance orbits because slightly
perturbed orbits define a corresponding two-dimensional invariant manifold on the Poincaré surface-section. For the resonance
orbit of the hyperbolic–elliptic type, we show numerically that its stable and unstable manifolds intersect transversally
in phase-space to induce instability. Then, we find indications that there are orbits which jump from one resonance zone to
the next before escaping to infinity. This phenomenon is related to the so-called Arnold diffusion.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
10.
We study the families of simple periodic orbits in a three-dimensional system that represents the inner parts of a perturbed triaxial galaxy. The perturbations depend on two control parameters. We find the regions where each family is stable, simply unstable, doubly unstable, or complex unstable. the stable and simply unstable families produce other families by bifurcation. Several families reach a maximum (or minimum) perturbation and then are continued by other families. The bifurcations are direct or inverse. The transition from one type of bifurcation to the other is theoretically explained. Another important phenomenon is the splitting of one family into two, or the joining of two families into one. We do not have any complex instability in the limiting cases of two-dimensional motions (when one control parameter is zero).The two main families of periodic orbits are in most cases stable when the energy is smaller than the escape energy. Most high energy orbits are unstable. However, we found stable orbits even for energies about four times larger than the escape energy. 相似文献
11.
B. Barbanis 《Celestial Mechanics and Dynamical Astronomy》1990,48(1):57-77
We investigate the escape regions of a quartic potential and the main types of irregular periodic orbits. Because of the symmetry of the model the zero velocity curve consists of four summetric arcs forming four open channels around the lines y = ± x through which an orbit can escape. Four unstable Lyapunov periodic orbits bridge these openings.We have found an infinite sequence of families of periodic orbits which is the outer boundary of one of the escape regions and several infinite sequences of periodic orbits inside this region that tend to homoclinic and heteroclinic orbits. Some of these sequences of periodic orbits tend to homoclinic orbits starting perpendicularly and ending asymptotically at the x-axis. The other sequences tend to heteroclinic orbits which intersect the x-axis perpendicularly for x > 0 and make infinite oscillations almost parallel to each of the two Lyapunov orbits which correspond to x > 0 or x < 0. 相似文献
12.
Noboru Takeichi 《Celestial Mechanics and Dynamical Astronomy》2010,108(4):405-416
The parametric excitation of a gravity gradient stabilized spacecraft induced by the periodic solar pressure torque is discussed.
The solar pressure torque in the linearized equations of motion appears as linear terms with periodic coefficients. The attitude
stability is analyzed numerically through the calculation of the Floquet multiplier. The perturbation method is also applied
to identify the instability condition analytically. It is made clear that the periodic solar pressure torque can destabilize
the coupled roll and yaw attitude motion of the spacecraft. It is also shown that the conditions of parametric resonance are
included in the gravity gradient stability condition. Nonlinear simulations are also carried out to verify the effect of the
parametric resonance. The numerical simulation using actual parameters shows that the spacecraft inevitably experiences a
large amplitude attitude motion due to the periodic solar pressure torque even if the gravity gradient stability condition
is satisfied. 相似文献
13.
Station-keeping for a translunar communication station 总被引：1，自引：0，他引：1
John V. Breakwell Ahmed A. Kamel Martin J. Ratner 《Celestial Mechanics and Dynamical Astronomy》1974,10(3):357-373
A translunar communication station is to be kept close to a nominal unstable periodic ‘Halo’ orbit, visible at all times from Earth. The analytically computed nominal orbit is not perfect, requiring an average control acceleration of about 10?6 g's for tight control. An adjustable quadratic combination of position deviation and control acceleration is minimized to provide an (adjustable) control law with period feedback gains and a periodic bias. The average control acceleration can be reduced to less than 10?8 g's with an error settling time of less than 21/2 months. The resulting limiting motion provides, in turn, an improved nominal, permitting the same low control cost with much tighter control, corresponding to settling times of the order of one day. 相似文献
14.
15.
The stability of attitude equilibria relative to gravitational torques for a rigid satellite in a circular orbit has been divided into three inertia regions, the Lagrange region of assured Liapunov stability, the Beletskii-Delp region which is often described as stabilized due to gyroscopic coupling, and an assured instability region. The generalization of these regions to the case of dual-spin or gyrostat satellites whose internal spin momentum is along a principal axis is treated here. The stability boundaries are obtained for all possible equilibrium orientations for such vehicles, and the variations of these boundaries corresponding to changes in the internal momentum magnitude, or to aligning the momentum with a different principal axis, are determined.Alexander von Humboldt Research Fellow at the Institut für Mechanik; on sabbatical leave from Columbia University, New York, U.S.A. 相似文献
16.
A problem of attitude motion of the smallest body for the restricted three-body problem is analyzed. Axial symmetry is assumed for the body, and attention is focused on the case in which the symmetry axis is normal to the orbit plane. For libration point satellites, results are similar to those for a satellite in orbit about a single body. However, for orbit equilibrium points lying on the line joining the two larger bodies, attitude stability results depart markedly from those for the two-body problem.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration. 相似文献
17.
P. C. Kammeyer 《Celestial Mechanics and Dynamical Astronomy》1980,22(3):289-296
In this paper three results on the linearized mapping associated with the plane three body problem near a periodic orbit are established. It is first shown that linear stability of such an orbit is independent of initial position on the orbit and of coordinate system. Second, the relation of Hénon connecting the rates of change of rotation angle and period on an isoenergetic family of periodic orbits is proved, together with a similar relation for families of orbits closing exactly in a rotating coordinate system. Finally, a condition for a critical orbit is given which is applicable to any family of periodic orbits. 相似文献
18.
Norbert Wex 《Monthly notices of the Royal Astronomical Society》1998,298(1):67-77
In binary radio pulsars with a main-sequence star companion, the spin-induced quadrupole moment of the companion gives rise to a precession of the binary orbit. As a first approximation one can model the secular evolution caused by this classical spin-orbit coupling by linear-in-time changes of the longitude of periastron and the projected semi-major axis of the pulsar orbit. This simple representation of the precession of the orbit neglects two important aspects of the orbital dynamics of a binary pulsar with an oblate companion. First, the quasiperiodic effects along the orbit, owing to the anisotropic 1/ r 3 nature of the quadrupole potential. Secondly, the long-term secular evolution of the binary orbit, which leads to an evolution of the longitude of periastron and the projected semi-major axis, which is non-linear in time. In this paper a simple timing formula for binary radio pulsars with a main-sequence star companion is presented which models the short-term secular and most of the short-term periodic effects caused by the classical spin-orbit coupling. I also give extensions of the timing formula that account for long-term secular changes in the binary pulsar motion. It is shown that the short-term periodic effects are important for the timing observations of the binary pulsar PSR B1259–63. The long-term secular effects are likely to become important in the next few years of timing observations of the binary pulsar PSR J0045–7319. They could help to restrict or even determine the moments of inertia of the companion star and thus probe its internal structure. Finally, I reinvestigate the spin-orbit precession of the binary pulsar PSR J0045–7319 since the analysis given in the literature is based on an incorrect expression for the precession of the longitude of periastron. A lower limit of 20° for the inclination of the B star with respect to the orbital plane is derived. 相似文献
19.
A. P. Markeev 《Astronomy Letters》2005,31(9):627-633
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
20.
A detailed derivation of the effect of solar radiation pressure on the orbit of a body about a primary orbiting the Sun is
given. The result is a set of secular equations that can be used for long-term predictions of changes in the orbit. Solar
radiation pressure is modeled as a Fourier series in the body’s rotation state, where the coefficients are based on the shape
and radiation properties of the body as parameters. In this work, the assumption is made that the body is in a synchronous
orbit about the primary and rotates at a constant rate. This model is used to write explicit variational equations of the
energy, eccentricity vector, and angular momentum vector for an orbiting body. Given that the effect of the solar radiation
pressure and the orbit are periodic functions, they are readily averaged over an orbit. Furthermore, the equations can be
averaged again over the orbit of the primary about the Sun to give secular equations for long-term prediction. This methodology
is applied to both circular and elliptical orbits, and the full equations for secular changes to the orbit in both cases are
presented. These results can be applied to natural systems, such as the binary asteroid system 1999 KW4, to predict their
evolution due to the Binary YORP effect, or to artificial Earth orbiting, nadir-pointing satellites to enable more precise
models for their orbital evolution. 相似文献