共查询到20条相似文献，搜索用时 31 毫秒
1.
Rodney L. Anderson Jeffrey S. Parker 《Celestial Mechanics and Dynamical Astronomy》2013,115(3):311-331
In this study, transfer trajectories from the Earth to the Moon that encounter the Moon at various flight path angles are examined, and lunar approach trajectories are compared to the invariant manifolds of selected unstable orbits in the circular restricted three-body problem. Previous work focused on lunar impact and landing trajectories encountering the Moon normal to the surface, and this research extends the problem with different flight path angles in three dimensions. The lunar landing geometry for a range of Jacobi constants is computed, and approaches to the Moon via invariant manifolds from unstable orbits are analyzed for different energy levels. 相似文献
2.
Kathryn E. Davis Rodney L. Anderson Daniel J. Scheeres George H. Born 《Celestial Mechanics and Dynamical Astronomy》2011,109(3):241-264
This paper presents a method to construct optimal transfers between unstable periodic orbits of differing energies using invariant
manifolds. The transfers constructed in this method asymptotically depart the initial orbit on a trajectory contained within
the unstable manifold of the initial orbit and later, asymptotically arrive at the final orbit on a trajectory contained within
the stable manifold of the final orbit. Primer vector theory is applied to a transfer to determine the optimal maneuvers required
to create the bridging trajectory that connects the unstable and stable manifold trajectories. Transfers are constructed between
unstable periodic orbits in the Sun–Earth, Earth–Moon, and Jupiter-Europa three-body systems. Multiple solutions are found
between the same initial and final orbits, where certain solutions retrace interior portions of the trajectory. All transfers
created satisfy the conditions for optimality. The costs of transfers constructed using manifolds are compared to the costs
of transfers constructed without the use of manifolds. In all cases, the total cost of the transfer is significantly lower
when invariant manifolds are used in the transfer construction. In many cases, the transfers that employ invariant manifolds
are three times more efficient, in terms of fuel expenditure, than the transfer that do not. The decrease in transfer cost
is accompanied by an increase in transfer time of flight. 相似文献
3.
A method for space mission trajectory design is presented in the form of a greedy global search algorithm. It uses invariant manifolds of unstable periodic orbits and its main advantage is that it performs a global search for the suitable legs of the invariant manifolds to be connected for a preliminary transfer design, as well as the appropriate points of the legs for maneuver application. The designed indirect algorithm bases the greedy choice on the optimality conditions that are assumed for the theoretical minimum transfer cost of a spacecraft when using invariant manifolds. The method is applied to a test case space mission design project in the Earth–Moon system and is found to compare favorably with previous techniques applied to the same project. 相似文献
4.
Low-energy, low-thrust transfers to the Moon 总被引：1，自引：0，他引：1
G. Mingotti F. Topputo F. Bernelli-Zazzera 《Celestial Mechanics and Dynamical Astronomy》2009,105(1-3):61-74
5.
The proposed method connects two unstable periodic orbits by employing trajectories of their associated invariant manifolds that are perturbed in two levels. A first level of velocity perturbations is applied on the trajectories of the discretized manifolds at the points where they approach the nominal unstable periodic orbit in order to accelerate them. A second level of structured velocity perturbations is applied to trajectories that have already been subjected to first level perturbations in order to approximately meet the necessary conditions for a low \(\varDelta \text {V}\) transfer. Due to this two-level perturbation approach, the number of the trajectories obtained is significantly larger compared with approaches that employ traditional invariant manifolds. For this reason, the problem of connecting two unstable periodic orbits through perturbed trajectories of their manifolds is transformed into an equivalent discrete optimization problem that is solved with a very low computational complexity algorithm that is proposed in this paper. Finally, the method is applied to a lunar observation mission of practical interest and is found to perform considerably better in terms of \(\varDelta \text {V}\) cost and time of flight when compared with previous techniques applied to the same project. 相似文献
6.
High-order solutions of invariant manifolds associated with libration point orbits in the elliptic restricted three-body system 总被引：1，自引：0，他引：1
Hanlun Lei Bo Xu Xiyun Hou Yisui Sun 《Celestial Mechanics and Dynamical Astronomy》2013,117(4):349-384
High-order analytical solutions of invariant manifolds, associated with Lissajous and halo orbits in the elliptic restricted three-body problem (ERTBP), are constructed in this paper. The equations of motion of ERTBP in the pulsating synodic coordinate system have five equilibrium points, and the three collinear libration points as well as the associated center manifolds are unstable. In our calculation, the general solutions of the invariant manifolds associated with Lissajous and halo orbits around collinear libration points are expressed as power series of five parameters: the orbital eccentricity, two amplitudes corresponding to the hyperbolic manifolds, and two amplitudes corresponding to the center manifolds. The analytical solutions up to arbitrary order are constructed by means of Lindstedt–Poincaré method, and then the center and invariant manifolds, transit and non-transit trajectories in ERTBP are all parameterized. Since the circular restricted three-body problem (CRTBP) is a particular case of ERTBP when the eccentricity is zero, the general solutions constructed in this paper can be reduced to describe the dynamics around the collinear libration points in CRTBP naturally. In order to check the validity of the series expansions constructed, the practical convergence of the series expansions up to different orders is studied. 相似文献
7.
Michael Dellnitz Oliver Junge Marcus Post Bianca Thiere 《Celestial Mechanics and Dynamical Astronomy》2006,95(1-4):357-370
Recently new techniques for the design of energy efficient trajectories for space missions have been proposed that are based on the circular restricted three body problem as the underlying mathematical model. These techniques exploit the structure and geometry of certain invariant sets and associated invariant manifolds in phase space to systematically construct energy efficient flight paths. In this paper, we extend this model in order to account for a continuously applied control force on the spacecraft as realized by certain low thrust propulsion systems. We show how the techniques for the trajectory design can be suitably augmented and compute approximations to trajectories for a mission to Venus. 相似文献
8.
The low-energy lunar trajectories with lunar flybys are investigated based on the Sun-Earth-Moon bicircular problem (BCP). The characteristics of the distribution of trajectories in the phase space are summarized. Using the invariant manifolds in the BCP system, the low-energy lunar trajectories with lunar flybys are sought. Then, take time as an augmented dimension in the phase space of a nonautonomous system, we present the state space map and reveal the distribution of these lunar trajectories in the phase space. Consequently, we find that the low-energy lunar trajectories exist as families, and that the every moment in the Sun-Earth-Moon synodic period can be the departure date. Finally, we analyse the velocity increment, transfer duration, and system energy for the different trajectory families, and obtain the velocity-impulse optimal family and the transfer-duration optimal family, respectively. 相似文献
9.
P. Pergola K. Geurts C. Casaregola M. Andrenucci 《Celestial Mechanics and Dynamical Astronomy》2009,105(1-3):19-32
Application of low thrust propulsion to interconnect ballistic trajectories on invariant manifolds associated with multiple circular restricted three body systems has been investigated. Sun-planet three body models have been coupled to compute the two ballistic trajectories, where electric propulsion is used to interconnect these trajectories as no direct intersection in the Poincarè sections exists. The ability of a low thrust to provide the energy change required to transit the spacecraft between two systems has been assessed for some Earth to Mars transfers. The approach followed consists in a planetary escape on the unstable manifold starting from a periodic orbit around one of the two collinear libration points near the secondary body. Following the planetary escape and the subsequent coasting phase, the electric thruster is activated and executes an ad-hoc thrusting phase. The complete transfer design, composed of the three discussed phases, and possible applications to Earth–Mars missions is developed where the results are outlined in this paper. 相似文献
10.
Yuan Ren Pierpaolo Pergola Elena Fantino Bianca Thiere 《Celestial Mechanics and Dynamical Astronomy》2012,112(1):1-21
Over the past three decades, ballistic and impulsive trajectories between libration point orbits (LPOs) in the Sun–Earth–Moon
system have been investigated to a large extent. It is known that coupling invariant manifolds of LPOs of two different circular
restricted three-body problems (i.e., the Sun–Earth and the Earth–Moon systems) can lead to significant mass savings in specific
transfers, such as from a low Earth orbit to the Moon’s vicinity. Previous investigations on this issue mainly considered
the use of impulsive maneuvers along the trajectory. Here we investigate the dynamical effects of replacing impulsive ΔV’s with low-thrust trajectory arcs to connect LPOs using invariant manifold dynamics. Our investigation shows that the use
of low-thrust propulsion in a particular phase of the transfer and the adoption of a more realistic Sun–Earth–Moon four-body
model can provide better and more propellant-efficient solution. For this purpose, methods have been developed to compute
the invariant tori and their manifolds in this dynamical model. 相似文献
11.
Integrability, one of the classic issues in galactic dynamics and in general in celestial mechanics, is here revisited in a Riemannian geometric framework, where Newtonian motions are seen as geodesics of suitable -mechanical- manifolds. The existence of constants of motion that entail integrability is associated with the existence of Killing tensor fields on the mechanical manifolds. Such tensor fields correspond to hidden symmetries of non-Noetherian kind. Explicit expressions for Killing tensor fields are given for the N = 2 Toda model, and for a modified Hénon-Heiles model, recovering the already known analytic expressions of the second conserved quantity besides energy for each model respectively. 相似文献
12.
Christos Efthymiopoulos George Contopoulos Matthaios Katsanikas 《Celestial Mechanics and Dynamical Astronomy》2014,119(3-4):331-356
It is known that the asymptotic invariant manifolds around an unstable periodic orbit in conservative systems can be represented by convergent series (Cherry, Proc Lond Math Soc ser 2, 27:151–170, 1926; Moser, Commun Pure Appl Math 9:673, 1956 and 11:257, 1958; Moser, Giorgilli, Discret Contin Dyn Syst 7:855, 2001). The unstable and stable manifolds intersect at an infinity of homoclinic points, generating a complicated homoclinic tangle. In the case of simple mappings it was found (Da Silva Ritter et al., Phys D 29:181, 1987) that the domain of convergence of the formal series extends to infinity along the invariant manifolds. This allows in practice the study of the homoclinic tangle using only series. However in the case of Hamiltonian systems, or mappings with a finite analyticity domain, the convergence of the series along the asymptotic manifolds is also finite. Here, we provide numerical indications that the convergence does not reach any homoclinic points. We discuss in detail the convergence problem in various cases and we find the degree of approximation of the analytical invariant manifolds to the real (numerical) manifolds as (i) the order of truncation of the series increases, and (ii) we use higher numerical precision in computing the coefficients of the series. Then we introduce a new method of series composition, by using action-angle variables, that allows the calculation of the asymptotic manifolds up to an a arbitrarily large extent. This is the first case of an analytic development that allows the computation of the invariant manifolds and their intersections in a Hamiltonian system for an extent long enough to allow the study of homoclinic chaos by analytical means. 相似文献
13.
Photogravitational Restricted Three-Body Problem (PGRTBP) is considered and halo orbits are generated in the vicinity of the Sun–Mars L1 Lagrangian point. Deviation of properties such as time period, size and velocity variation in the halo orbits with Sun as a source of radiation are discussed. With increase in solar radiation pressure, the halo orbits are found to elongate and move towards the Sun and the time period of the halo orbits is found to increase. The variation in the behaviour of invariant manifolds with change in radiation pressure is also computed and it is found that as the radiation pressure increases, the transition from Mars-centric path to heliocentric path is delayed. Certain implications of the velocity profile of the invariant manifolds are also discussed. 相似文献
14.
Evan S. Gawlik Jerrold E. Marsden Philip C. Du Toit Stefano Campagnola 《Celestial Mechanics and Dynamical Astronomy》2009,103(3):227-249
This study investigates Lagrangian coherent structures (LCS) in the planar elliptic restricted three-body problem (ER3BP),
a generalization of the circular restricted three-body problem (CR3BP) that asks for the motion of a test particle in the
presence of two elliptically orbiting point masses. Previous studies demonstrate that an understanding of transport phenomena
in the CR3BP, an autonomous dynamical system (when viewed in a rotating frame), can be obtained through analysis of the stable
and unstable manifolds of certain periodic solutions to the CR3BP equations of motion. These invariant manifolds form cylindrical
tubes within surfaces of constant energy that act as separatrices between orbits with qualitatively different behaviors. The
computation of LCS, a technique typically applied to fluid flows to identify transport barriers in the domains of time-dependent
velocity fields, provides a convenient means of determining the time-dependent analogues of these invariant manifolds for
the ER3BP, whose equations of motion contain an explicit dependency on the independent variable. As a direct application,
this study uncovers the contribution of the planet Mercury to the Interplanetary Transport Network, a network of tubes through
the solar system that can be exploited for the construction of low-fuel spacecraft mission trajectories.
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. 相似文献
15.
Martin Lara 《Celestial Mechanics and Dynamical Astronomy》2017,127(3):285-300
This study analyzes a recently discovered class of exterior transfers to the Moon. These transfers terminate in retrograde ballistic capture orbits, i.e., orbits with negative Keplerian energy and angular momentum with respect to the Moon. Yet, their Jacobi constant is relatively low, for which no forbidden regions exist, and the trajectories do not appear to mimic the dynamics of the invariant manifolds of the Lagrange points. This paper shows that these orbits shadow instead lunar collision orbits. We investigate the dynamics of singular, lunar collision orbits in the Earth–Moon planar circular restricted three-body problem, and reveal their rich phase space structure in the medium-energy regime, where invariant manifolds of the Lagrange point orbits break up. We show that lunar retrograde ballistic capture trajectories lie inside the tube structure of collision orbits. We also develop a method to compute medium-energy transfers by patching together orbits inside the collision tube and those whose apogees are located in the appropriate quadrant in the Sun–Earth system. The method yields the novel family of transfers as well as those ending in direct capture orbits, under particular energetic and geometrical conditions. 相似文献
16.
Temporary satellite capture (TSC) of Jupiter-family comets has been a focus of investigation within the astronomy community for decades. More recently, TSC has been approached from the perspective of dynamical systems theory, within the context of the circular restricted three-body problem (CR3BP). Thus, this problem serves as a testbed for exploring techniques that support trajectory design in similar dynamical regimes. In particular, an association between the invariant manifolds of libration point orbits and the paths of comets that experience TSC has been explored. In this investigation, TSC is further examined from the perspective of transit, that is, transition through the gateways associated with the collinear libration points, in the three-body problem. Periapsis Poincaré maps, previously employed for trajectory design in several investigations, are used to deliver insight into the nature of transit trajectories for energy levels near those associated with several Jupiter-family comets. The evolution of transit trajectories with increasing energy is explored, and the existence of solutions with similar characteristics to the paths of comets P/1996 R2, 82P/Gehrels 3, and 147P/Kushida–Muramatsu is demonstrated within the context of the planar CR3BP using planar periapsis maps. During TSC, the path of comet 111P/Helin–Roman–Crockett is highly inclined with respect to Jupiter; the motion of this comet is examined relative to invariant manifolds in the spatial CR3BP. A method to display the information contained in higher-dimensional Poincaré maps is also demonstrated, and is employed to locate a trajectory possessing the same qualitative characteristics as the path of 111P/Helin–Roman–Crockett. 相似文献
17.
In this paper, a method to capture near-Earth objects (NEOs) incorporating low-thrust propulsion into the invariant manifolds technique is investigated. Assuming that a tugboat-spacecraft is in a rendez-vous condition with the candidate asteroid, the aim is to take the joint spacecraft-asteroid system to a selected periodic orbit of the Sun–Earth restricted three-body system: the orbit can be either a libration point periodic orbit (LPO) or a distant prograde periodic orbit (DPO) around the Earth. In detail, low-thrust propulsion is used to bring the joint spacecraft-asteroid system from the initial condition to a point belonging to the stable manifold associated to the final periodic orbit: from here onward, thanks to the intrinsic dynamics of the physical model adopted, the flight is purely ballistic. Dedicated guided and capture sets are introduced to exploit the combined use of low-thrust propulsion with stable manifolds trajectories, aiming at defining feasible first guess solutions. Then, an optimal control problem is formulated to refine and improve them. This approach enables a new class of missions, whose solutions are not obtainable neither through the patched-conics method nor through the classic invariant manifolds technique. 相似文献
18.
Ernesto A. Lacomba Ernesto Pérez-Chavela 《Celestial Mechanics and Dynamical Astronomy》1993,57(3):411-437
In this work we study escape and capture orbits in the planar rhomboidal 4-body problem in a level of constant negative energy. There are only two different values of the masses here. By using numerical analysis, we show certain transversal intersections of the invariant manifolds of parabolic orbits. We then introduce Symbolic Dynamics when the mass ratio is small, and when it is close to one. In the first case the escapes or captures predominate in the direction of one of the diagonals of the rhombus, while in the second case we find solutions escaping or being captured in the direction of both possible diagonals. 相似文献
19.
P. Tsoutsis C. Efthymiopoulos N. Voglis † 《Monthly notices of the Royal Astronomical Society》2008,387(3):1264-1280
In a previous paper (Voglis et al., Paper I), we demonstrated that, in a rotating galaxy with a strong bar, the unstable asymptotic manifolds of the short-period family of unstable periodic orbits around the Lagrangian points L 1 or L 2 create correlations among the apocentric positions of many chaotic orbits, thus supporting a spiral structure beyond the bar. In this paper, we present evidence that the unstable manifolds of all the families of unstable periodic orbits near and beyond corotation contribute to the same phenomenon. Our results refer to a N -body simulation, a number of drawbacks of which, as well as the reasons why these do not significantly affect the main results, are discussed. We explain the dynamical importance of the invariant manifolds as due to the fact that they produce a phenomenon of 'stickiness' slowing down the rate of chaotic escape in an otherwise non-compact region of the phase space. We find a stickiness time of the order of 100 dynamical periods, which is sufficient to support a long-living spiral structure. Manifolds of different families become important at different ranges of values of the Jacobi constant. The projections of the manifolds of all the different families in the configuration space produce a pattern due to the 'coalescence' of the invariant manifolds. This follows closely the maxima of the observed m = 2 component near and beyond corotation. Thus, the manifolds support both the outer edge of the bar and the spiral arms. 相似文献
20.
R. C. Calleja E. J. Doedel A. R. Humphries A. Lemus-Rodríguez E. B. Oldeman 《Celestial Mechanics and Dynamical Astronomy》2012,114(1-2):77-106
We demonstrate the remarkable effectiveness of boundary value formulations coupled to numerical continuation for the computation of stable and unstable manifolds in systems of ordinary differential equations. Specifically, we consider the circular restricted three-body problem (CR3BP), which models the motion of a satellite in an Earth–Moon-like system. The CR3BP has many well-known families of periodic orbits, such as the planar Lyapunov orbits and the non-planar vertical and halo orbits. We compute the unstable manifolds of selected vertical and halo orbits, which in several cases leads to the detection of heteroclinic connections from such a periodic orbit to invariant tori. Subsequent continuation of these connecting orbits with a suitable end point condition and allowing the energy level to vary leads to the further detection of apparent homoclinic connections from the base periodic orbit to itself, or the detection of heteroclinic connections from the base periodic orbit to other periodic orbits. Some of these connecting orbits are of potential interest in space mission design. 相似文献