共查询到20条相似文献，搜索用时 93 毫秒
1.
This paper discusses a numerical searching approach for the relative motion of formation flying in displaced orbits by spacecraft with low-thrust propulsion. The nonlinear dynamical model of spacecraft is established in a two-body rotating reference frame with arbitrary polar component of momentum and thrust-induced acceleration. Motions near the stable equilibria are distinguished from each other by means of five-dimensional variables, which can then be compressed uniquely into two-dimensional mapping images characterized by the crossing interval and the angle drifts. The surjective but not injective mapping makes the generation of three configurations of the relative motions possible. The corresponding relative orbits for three kinds of two-spacecraft formation flying are searched and exemplified based on the formation conditions formulized as functions of the crossing interval and the angle drifts. Furthermore, based on the assignment of displaced relative orbits to five-dimensional vector, the working orbit of the deputy for a specific chief can also be searched via the optimization algorithm to generate the bounded relative motion with the minimum thrust acceleration magnitude, which is of certain significance in reducing fuel consumption of formations. 相似文献
2.
Marco Giancotti Mauro Pontani Paolo Teofilatto 《Celestial Mechanics and Dynamical Astronomy》2012,114(1-2):55-76
Analysis and design of low-energy transfers to the Moon has been a subject of great interest for many decades. This paper is concerned with a topological study of such transfers, with emphasis to trajectories that allow performing lunar capture and those that exhibit homoclinic connections, in the context of the circular restricted three-body problem. A fundamental theorem stated by Conley locates capture trajectories in the phase space and can be condensed in a sentence: “if a crossing asymptotic orbit exists then near any such there is a capture orbit”. In this work this fundamental theoretical assertion is used together with an original cylindrical isomorphic mapping of the phase space associated with the third body dynamics. For a given energy level, the stable and unstable invariant manifolds of the periodic Lyapunov orbit around the collinear interior Lagrange point are computed and represented in cylindrical coordinates as tubes that emanate from the transformed periodic orbit. These tubes exhibit complex geometrical features. Their intersections correspond to homoclinic orbits and determine the topological separation of long-term lunar capture orbits from short-duration capture trajectories. The isomorphic mapping is proven to allow a deep insight on the chaotic motion that characterizes the dynamics of the circular restricted three-body, and suggests an interesting interpretation, and together corroboration, of Conley’s assertion on the topological location of lunar capture orbits. Moreover, an alternative three-dimensional representation of the phase space is profitably employed to identify convenient lunar periodic orbits that can be entered with modest propellant consumption, starting from the Lyapunov orbit. 相似文献
3.
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
4.
Stephen B. Broschart Gregory Lantoine Daniel J. Grebow 《Celestial Mechanics and Dynamical Astronomy》2014,120(2):195-215
Quasi-terminator orbits are introduced as a class of quasi-periodic trajectories in the solar radiation pressure (SRP) perturbed Hill dynamics. These orbits offer significant displacements along the Sun-direction without the need for station-keeping maneuvers. Thus, quasi-terminator orbits have application to primitive-body mapping missions, where a variety of observation geometries relative to the Sun (or other directions) can be achieved. This paper describes the characteristics of these orbits as a function of normalized SRP strength and invariant torus frequencies and presents a discussion of mission design considerations for a global surface mapping orbit design. 相似文献
5.
There exist many comets with near-parabolic orbits in the Solar System. Among various theories proposed to explain their origin, the Oort cloud hypothesis seems to be the most reasonable (Oort, 1950). The theory assumes that there is a cometary cloud at a distance 103 – 105 AU from the Sun and that perturbing forces from planets or stars make orbits of some of these comets become of near-parabolic type. Concerning the evolution of these orbits under planetary perturbations, we can raise the question: Will they stay in the Solar System forever or will they escape from it? This is an attractive dynamical problem. If we go ahead by directly solving the dynamical differential equations, we may encounter the difficulty of long-time computation. For the orbits of these comets are near-parabolic and their periods are too long to study on their long-term evolution. With mapping approaches the difficulty will be overcome. In another aspect, the study of this model has special meaning for chaotic dynamics. We know that in the neighbourhood of any separatrix i.e. the trajectory with zero frequency of the unperturbed motion of an Hamiltonian system, some chaotic motions have to be expected. Actually, the simplest example of separatrix is the parabolic trajectory of the two body problem which separates the bounded and unbounded motion. From this point of view, the dynamical study on near-parabolic motion is very important. Petrosky's elegant but more abstract deduction gives a Kepler mapping which describes the dynamics of the cometary motion (Petrosky, 1988). In this paper we derive a similar mapping directly and discuss its dynamical characters. 相似文献
6.
We consider the motions of particles in the one-dimensional Newtonian three-body problem as a function of initial values.
Using a mapping of orbits to symbol sequences we locate the initial values leading to triple collisions. These turn out to
form curves which give clear structure to the region in which the motions depend sensitively on initial conditions. In addition
to finding the triple collision orbits we also locate orbits which end up to a triple collision in both directions of time,
that is, orbits which are finite both in space and time.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
7.
N. D. Caranicolas 《Celestial Mechanics and Dynamical Astronomy》1989,47(1):87-96
We derive an algebraic mapping for an autonomous, two-dimensional galactic type Hamiltonian in the 1/1 resonance case. We use the mapping to study the stability of the periodic orbits. Using the x — p
x
Poincaré surface section, we compare the results of the mapping with those found by the numerical integration of the full equations of motion. For small values of the perturbation the results of the two methods are in very good agreement while satisfactory agreement is obtained for larger perturbations. 相似文献
8.
Marco Giancotti Mauro Pontani Paolo Teofilatto 《Celestial Mechanics and Dynamical Astronomy》2014,120(3):249-268
Several families of periodic orbits exist in the context of the circular restricted three-body problem. This work studies orbital motion of a spacecraft among these periodic orbits in the Earth–Moon system, using the planar circular restricted three-body problem model. A new cylindrical representation of the spacecraft phase space (i.e., position and velocity) is described, and allows representing periodic orbits and the related invariant manifolds. In the proximity of the libration points, the manifolds form a four-fold surface, if the cylindrical coordinates are employed. Orbits departing from the Earth and transiting toward the Moon correspond to the trajectories located inside this four-fold surface. The isomorphic mapping under consideration is also useful for describing the topology of the invariant manifolds, which exhibit a complex geometrical stretch-and-folding behavior as the associated trajectories reach increasing distances from the libration orbit. Moreover, the cylindrical representation reveals extremely useful for detecting periodic orbits around the primaries and the libration points, as well as the possible existence of heteroclinic connections. These are asymptotic trajectories that are ideally traveled at zero-propellant cost. This circumstance implies the possibility of performing concretely a variety of complex Earth–Moon missions, by combining different types of trajectory arcs belonging to the manifolds. This work studies also the possible application of manifold dynamics to defining a suitable, convenient end-of-life strategy for spacecraft placed in any of the unstable orbits. The final disposal orbit is an externally confined trajectory, never approaching the Earth or the Moon, and can be entered by means of a single velocity impulse (of modest magnitude) along the right unstable manifold that emanates from the Lyapunov orbit at \(L_2\) . 相似文献
9.
The present paper addresses the existence of J
2 invariant relative orbits with arbitrary relative magnitude over the infinite time using the Routh reduction and Poincaré
techniques in the J
2 Hamiltonian problem. The current research also proposes a novel numerical searching approach for J
2 invariant relative orbits from the dynamical system point of view. A new type of Poincaré mapping is defined from different
central manifolds of the pseudo-circular orbits (parameterized by the Jacobi energy E, the polar component of momentum H
z
and the measure of distance Δr between the fixed point and its central manifolds) to the nodal periods T
d
and the drifts of longitude of the ascending node during one period (ΔΩ), which differs from Koon et al.’s (AIAA 2001) definition on central manifolds parameterized by the same fixed point. The Poincaré mapping is surjective because it compresses
the three-dimensional variables into two-dimensional images, and the mapping degenerates into a bijective mapping in consideration
of the fixed points. An iteration algorithm to the degenerated bijective mapping is proposed from the continuation procedure
to perform the ergodic representation of E- and H
z
-contour maps on the space of T
d
–ΔΩ. For the surjective mapping with Δr ≠ 0, different pseudo-circular or elliptical orbits may share the same images. Hence, the inverse surjective mapping may
achieve non-unique variables from a single image, which makes the generation of J
2 invariant relative orbits possible. The pseudo-circular or elliptical orbits generated from the surjective mapping will be
defined in different meridian planes. Hence, the critical contribution of the present paper is the assignment of J
2 invariant relative orbits to different invariant parameters E and H
z
depending on the E- and H
z
-contour map, which will hold J
2 invariant relative orbits for extended durations. To investigate the high-order nonlinearity neglected by previous studies,
a formation configuration with a large magnitude of 500 km is successfully generated from the theory developed in the present
work, which is beyond the scope of the linear conditions of J
2 invariant relative orbits. Therefore, the existence of J
2 invariant relative orbit with an arbitrary relative magnitude over the infinite time is achieved from the dynamical system
point of view. 相似文献
10.
V.S. Kalantonis E.A. Perdios A.E. Perdiou O. Ragos M.N. Vrahatis 《Astrophysics and Space Science》2003,288(4):489-497
The computation of periodic orbits of nonlinear mappings or dynamical systems can be achieved by applying a root-finding method. To determine a periodic solution, an initial guess should be located within a proper area of the mapping or a surface of section of the phase space of the dynamical system. In the case of Newton or Newton-like methods these areas are the basins of convergence corresponding to the considered solution. When several solutions of the same period exist in a particular region, then the deflation technique is suitable for the calculation of all these solutions. This technique is applied here to the Hénon's mapping and the driven conservative Duffing's oscillator. 相似文献
11.
The propagation and Poincaré mapping of perturbed Keplerian motion is a key topic in Celestial Mechanics and Astrodynamics, e.g., to study the stability of orbits or design bounded relative trajectories. The high-order transfer map (HOTM) method enables efficient mapping of perturbed Keplerian orbits using the high-order Taylor expansion of a Poincaré or stroboscopic map. The HOTM is only accurate close to the expansion point and therefore the number of revolutions for which the map is accurate tends to be limited. The proper selection of coordinates is of key importance for improving the performance of the HOTM method. In this paper, we investigate the use of different element sets for expressing the high-order map in order to find the coordinates that perform best in terms of accuracy. A new set of elements is introduced that enables extremely accurate mapping of the state, even for high eccentricities and higher-order zonal perturbations. Finally, the high-order map is shown to be very useful for the determination and study of fixed points and center manifolds of Poincaré maps. 相似文献
12.
我们已经研究了分别具椭圆和双曲不动点的二维保测度映射及其受摄三维扩张的ＫＳ熵。本文研究一类具抛物不动点的二维保测度映射：及其受摄扩张：的ＫＳ熵随参数Ａ、Ｂ、Ｃ、Ｄ、Ｅ的变化．数值探索结果表明：适当定义区域内的二维映射Ｔ２的ＫＳ熵与Ａ无关，与我们的理论分析结果相一致。受摄扩张映射Ｔ３的ＫＳ熵随摄动参数Ｂ、Ｃ、Ｄ的增大而增大，却随Ｅ的增大而减小．我们还发现，随着摄动的逐渐增强，映射Ｔ３的不变环面将逐渐破裂，使更多的轨道逃逸，从而可能使映射Ｔ３的ＫＳ熵减小。另外，不变环面存在的判别式在大范围内仍在一定程度上有效。 相似文献
13.
V. A. Shefer 《Astronomy Letters》2006,32(12):845-858
The theory of superosculating intermediate orbits previously suggested by the author is developed. A new class of orbits with a fourth-order tangency to the actual trajectory of a celestial body at the initial time is constructed. Orbits with a fifth-order tangency have been constructed for the first time. The motion in the constructed orbits is represented as a combination of two motions: the motion of a fictitious attracting center with a variable mass and the motion relative to this center. The first motion is generally parabolic, while the second motion is described by the equations of the Gylden—Mestschersky problem. The variation in the mass of the fictitious center obeys Mestschersky’s first and combined laws. The new orbits represent more accurately the actual motion in the initial segment of the trajectory than an osculating Keplerian orbit and other existing analogues. Encke’s generalized methods of special perturbations in which the constructed intermediate orbits are used as reference orbits are presented. Numerical simulations using the approximations of the motions of Asteroid Toutatis and Comet P/Honda—Mrkos—Pajdu?áková as examples confirm that the constructed orbits are highly efficient. Their application is particularly beneficial in investigating strongly perturbed motion. 相似文献
14.
In the current study, the existence of periodic orbits around a fixed homogeneous cube is investigated, and the results have
powerful implications for examining periodic orbits around non-spherical celestial bodies. In the two different types of symmetry
planes of the fixed cube, periodic orbits are obtained using the method of the Poincaré surface of section. While in general
positions, periodic orbits are found by the homotopy method. The results show that periodic orbits exist extensively in symmetry
planes of the fixed cube, and also exist near asymmetry planes that contain the regular Hex cross section. The stability of
these periodic orbits is determined on the basis of the eigenvalues of the monodromy matrix. This paper proves that the homotopy
method is effective to find periodic orbits in the gravity field of the cube, which provides a new thought of searching for
periodic orbits around non-spherical celestial bodies. The investigation of orbits around the cube could be considered as
the first step of the complicated cases, and helps to understand the dynamics of orbits around bodies with complicated shapes.
The work is an extension of the previous research work about the dynamics of orbits around some simple shaped bodies, including
a straight segment, a circular ring, an annulus disk, and simple planar plates. 相似文献
15.
Demands for a broad range of integrated geospatial data-analysis tools and methods for planetary data organization have been growing considerably since the late 1990s when a plethora of missions equipped with new instruments entered planetary orbits or landed on the surface. They sent back terabytes of new data which soon became accessible for the scientific community and public and which needed to be organized. On the terrestrial side, issues of data access, organization and utilization for scientific and economic analyses are handled by using a range of well-established geographic information systems (GIS) that also found their way into the field of planetary sciences in the late 1990s. We here address key issues concerning the field of planetary mapping by making use of established GIS environments and discuss methods of addressing data organization and mapping requirements by using an easily integrable datamodel that is—for the time being—designed as file-geodatabase (FileGDB) environment in ESRI's ArcGIS. A major design-driving requirement for this datamodel is its extensibility and scalability for growing scientific as well as technical needs, e.g., the utilization of such a datamodel for surface mapping of different planetary objects as defined by their respective reference system and by using different instrument data. Furthermore, it is a major goal to construct a generic model which allows to perform combined geologic as well as geomorphologic mapping tasks making use of international standards without loss of information and by maintaining topologic integrity. An integration of such a datamodel within a geospatial DBMS context can practically be performed by individuals as well as groups without having to deal with the details of administrative tasks and data ingestion issues. Besides the actual mapping, key components of such a mapping datamodel deal with the organization and search for image-sensor data and previous mapping efforts, as well as the proper organization of cartographic representations and assignments of geologic/geomorphologic units within their stratigraphic context. 相似文献
16.
Alessandra Celletti Gabriella Della Penna Claude Froeschlé 《Celestial Mechanics and Dynamical Astronomy》2002,83(1-4):257-274
We investigate the break-down threshold of librational invariant curves. As a model problem, we consider a variant of a mapping introduced by M. Hénon, which well describes the dynamics of librational motions surrounding a stable invariant point. We verify in concrete examples the applicability of Greene's method, by computing the instability transition values of a sequence of periodic orbits approaching an invariant curve with fixed noble frequency. However, this method requires the knowledge of the location of the periodic orbits within a very good approximation. This task appears to be difficult to realize for a libration regime, due to the different topology of the phase space. To compute the break-down threshold, we tried an alternative method very easy to implement, based on the computation of the fast Lyapunov indicators and frequency analysis. Such technique does not require the knowledge of the periodic orbits, but again, it appears very difficult to have a precision better than Greene's method for the computation of the critical parameter. 相似文献
17.
Winston L. Sweatman 《Celestial Mechanics and Dynamical Astronomy》2006,94(1):37-65
We locate members of an important category of periodic orbits in the Newtonian four-body problem. These systems perform an interplay motion similar to that of the periodic three-body orbit discovered by Schubart. Such orbits, when stable, have been shown to be a key feature and influence on the dynamics of few-body systems. We consider the restricted case where the masses are collinear and are distributed symmetrically about their centre of mass. A family of orbits is generated from the known (three-dimensionally) unstable equal masses case by varying the mass ratio, whilst maintaining the symmetry. The stability of these orbits to perturbation is studied using linear stability analysis, analytical approximation of limiting cases and nonlinear simulation. We answer the natural question: are there any stable periodic orbits of this kind? Three ranges of the mass ratio are found to have stable orbits and three ranges have unstable orbits for three-dimensional motion. The systems closely resemble their three-body counterparts. Here the family of interplay orbits is simpler requiring just one parameter to characterise the mass ratio. Our results provide a further insight into three-body orbits studied previously. 相似文献
18.
We study analytically the orbits along the asymptotic manifolds from a complex unstable periodic orbit in a symplectic 4-D Froeschlé map. The orbits are given as convergent series. We compare the analytic results by truncating the series at various orders with the corresponding numerical results and we find agreement along a more extended length, as the order of truncation increases. The agreement is improved when the parameters approach those of the stability domain. Along the manifolds no terms with small divisors appear in the series. The same result is found if we use a parametrization method along the asymptotic curves. In the case of orbits starting close to the manifolds small divisors appear, but the orbits remain close to the manifolds for an extended period of time. If the parameters of the map are close to the stable domain the orbits recede and approach the origin several times and remain confined in a certain volume around the origin for a long time before escaping to large distances. For special sets of parameters we see resonance phenomena and the orbits take particular forms near every resonance. 相似文献
19.
We analyze four-dimensional symplectic mappings in the neighbourhood of an elliptic fixed point whose eigenvalues are close
to satisfy a third-order resonance. Using the perturbative tools of resonant normal forms, the geometry of the orbits and
the existence of elliptic or hyperbolic one-dimensional tori (fixed lines) is worked out. This allows one to give an analytical
estimate of the stability domain when the resonance is unstable. A comparison with numerical results for the four-dimensional
Hénon mapping is given.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
20.
P.G. Welch 《Monthly notices of the Royal Astronomical Society》2001,328(1):101-111
A new search method for locating meteoroid streams within an orbit data base and obtaining their central core orbits is introduced. The method is based on the transformation of a data base of discrete orbits into a continuous density map. Artificial data bases are used to determine if a density is statistically unlikely to occur by random chance. A search is then run to identify all density peaks within the map that correspond to the central core of a meteoroid stream. Drummond D' criterion is used as a metric within the transformation and a D' acceptability limit, D l , defines the length scale over which a discrete meteor orbit can have an influence on the density map. Examination of the search dependence on D l for both real and artificial data sets indicates an appropriate standard value. A full search is run on 5280 meteor orbits from the IAU data base, detecting 16 known major and minor meteoroid streams. New central core orbits are presented for these. No major differences from the published orbits are detected, apart from possible multi-branched structure in the southern δ Aquarids. 相似文献