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1.
Impulsive time-free transfers between halo orbits 总被引：1，自引：0，他引：1
A methodology is developed to design optimal time-free impulsive transfers between three-dimensional halo orbits in the vicinity of the interior L
1 libration point of the Sun-Earth/Moon barycenter system. The transfer trajectories are optimal in the sense that the total characteristic velocity required to implement the transfer exhibits a local minimum. Criteria are established whereby the implementation of a coast in the initial orbit, a coast in the final orbit, or dual coasts accomplishes a reduction in fuel expenditure. The optimality of a reference two-impulse transfer can be determined by examining the slope at the endpoints of a plot of the magnitude of the primer vector on the reference trajectory. If the initial and final slopes of the primer magnitude are zero, the transfer trajectory is optimal; otherwise, the execution of coasts is warranted. The optimal time of flight on the time-free transfer, and consequently, the departure and arrival locations on the halo orbits are determined by the unconstrained minimization of a function of two variables using a multivariable search technique. Results indicate that the cost can be substantially diminished by the allowance for coasts in the initial and final libration-point orbits.An earlier version was presented as Paper AIAA 92-4580 at the AIAA/AAS Astrodynamics Conference, Hilton Head Island, SC, U.S.A., August 10–12, 1992. 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.
Lawden’s primer vector theory gives a set of necessary conditions that characterize the optimality of a transfer orbit, defined accordingly to the possibility of adding mid-course corrections. In this paper a novel approach is proposed where, through a polar coordinates transformation, the primer vector components decouple. Furthermore, the case when transfer, departure and arrival orbits are coplanar is analyzed using a Hamiltonian approach. This procedure leads to approximate analytic solutions for the in-plane components of the primer vector. Moreover, the solution for the circular transfer case is proven to be the Hill’s solution. The novel procedure reduces the mathematical and computational complexity of the original case study. It is shown that the primer vector is independent of the semi-major axis of the transfer orbit. The case with a fixed transfer trajectory and variable initial and final thrust impulses is studied. The acquired related optimality maps are presented and analyzed and they express the likelihood of a set of trajectories to be optimal. Furthermore, it is presented which kind of requirements have to be fulfilled by a set of departure and arrival orbits to have the same profile of primer vector. 相似文献
4.
The use of invariant manifolds for transfers between unstable periodic orbits of different energies 总被引：1，自引：0，他引：1
Kathryn E. Davis Rodney L. Anderson Daniel J. Scheeres George H. Born 《Celestial Mechanics and Dynamical Astronomy》2010,107(4):471-485
Techniques from dynamical systems theory have been applied to the construction of transfers between unstable periodic orbits
that have different energies. Invariant manifolds, trajectories that asymptotically depart or approach unstable periodic orbits,
are used to connect the initial and final orbits. The transfer asymptotically departs the initial orbit on a trajectory contained
within the initial orbit’s unstable manifold and later asymptotically approaches the final orbit on a trajectory contained
within the stable manifold of the final orbit. The manifold trajectories are connected by the execution of impulsive maneuvers.
Two-body parameters dictate the selection of the individual manifold trajectories used to construct efficient transfers. A
bounding sphere centered on the secondary, with a radius less than the sphere of influence of the secondary, is used to study
the manifold trajectories. A two-body parameter, κ, is computed within the bounding sphere, where the gravitational effects of the secondary dominate. The parameter κ is defined as the sum of two quantities: the difference in the normalized angular momentum vectors and eccentricity vectors
between a point on the unstable manifold and a point on the stable manifold. It is numerically demonstrated that as the κ parameter decreases, the total cost to complete the transfer decreases. Preliminary results indicate that this method of
constructing transfers produces a significant cost savings over methods that do not employ the use of invariant manifolds. 相似文献
5.
A first-order minimum propellant guidance law is developed for multi-impulse trajectories in an inverse-square gravitational field. A second-order variational analysis is used to formulate the guidance problem as an accessory minimum problem, i.e. minimize a quadratic form (second-variation in propellant consumption) subject to linear constraints (variational equations of motion and deterministic boundary conditions). Solution of the accessory minimum problem provides the optimal guidance law in feedback form. It is emphasized that this analysis takes into account the nominal impulse programme when calculating the optimal guidance corrections. It is shown that for multi-impulse transfers it is in general, non-optimal to add impulses. All corrections to the trajectory should be made by a combination of small changes in timing, magnitude and direction of the nominal impulses. 相似文献
6.
We discuss the consequences of momentum conservation in processes related to solar flares and coronal mass ejections (CMEs),
in particular describing the relative importance of vertical impulses that could contribute to the excitation of seismic waves
(“sunquakes”). The initial impulse associated with the primary flare energy transport in the impulsive phase contains sufficient
momentum, as do the impulses associated with the acceleration of the evaporation flow (the chromospheric shock) or the CME
itself. We note that the deceleration of the evaporative flow, as coronal closed fields arrest it, will tend to produce an
opposite impulse, reducing the energy coupling into the interior. The actual mechanism of the coupling remains unclear at
present. 相似文献
7.
H. Hiller 《Planetary and Space Science》1965,13(12):1233-1247
A study has been made of optimum transfers between elliptic and non-coplanar circular orbits having a common centre of attraction and whose planes intersect along the major axis of the ellipse. Elliptic transfer paths with up to three apsidal impulses are considered, with the whole plane change taking place at the (coincident) apocentres of these paths.
For three-impulse transfers, the optimum mode is always to transfer from the pericentre of the elliptic orbit to the circular orbit, or vice-versa. For the two-impulse “tilted-Hohmann” type of transfer, the optimum mode for the ellipse-in-circle arrangement of initial and final orbits is also to transfer from pericentre to circle; but the optimum mode is from apocentre to circle for both the circle-in-ellipse and overlap arrangements. 相似文献
8.
《天文和天体物理学研究(英文版)》2021,(6)
The high area/mass ratio hopping rovers have potential applications in future asteroid surface exploration. This paper systematically investigates the effects of solar radiation pressure(SRP) on ballistic surface hopping transfers for the asteroid 101955 Bennu. Effects of SRP on the traveled distance and the trajectory design of hopping transfers are analyzed and summarized. The simulation results indicate that it is necessary to take SRP into account to ensure the success of hopping transfers and the proper use of SRP can help design the trajectories of hopping transfers with low initial impulses and short transfer times. It also reveals the potential possibility in using SRP to control the post-hopping transfers with specific control policies in the future surface exploration of asteroids. 相似文献
9.
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
10.
Priscilla Sousa-Silva Maisa O. Terra Matteo Ceriotti 《Astrophysics and Space Science》2018,363(10):210
This contribution deals with fast Earth–Moon transfers with ballistic capture in the patched three-body model. We compute ensembles of preliminary solutions using a model that takes into account the relative inclination of the orbital planes of the primaries. The ballistic capture orbits around the Moon are obtained relying on the hyperbolic invariant structures associated to the collinear Lagrangian points of the Earth–Moon system, and the Sun–Earth system portion of the transfers are quasi-periodic orbits obtained by a genetic algorithm. The trajectories are designed to be good initial guesses to search optimal cost-efficient short-time Earth–Moon transfers with ballistic capture in more realistic models. 相似文献
11.
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
12.
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
13.
Andrea Bolle Christian Circi Giuseppe Corrao 《Celestial Mechanics and Dynamical Astronomy》2010,106(2):183-196
Interplanetary transfers represent one of the most interesting themes of astrodynamics, because of its complexity and outcomes
for human exploration of the Solar System. A wide number of works concerning different aspects of the interplanetary mission
have been developed. The examination of these works leads to the conclusion that, by far, there is not a preferential propulsion
system or an optimal trajectory to perform an interplanetary mission, but a precise kind of transfer according to a given
mission profile. Here, minimum time trajectories to Mars for small payload transportation with different electric propulsion
systems have been analyzed; results have been obtained considering the initial impulse given by the Ariane 5 upper stage.
Additionally, an adaptative, multiple shooting optimization algorithm is proposed to solve the problem of optimality in interplanetary
transfers with a low continuous thrust. The algorithm searches for the optimal set of initial Lagrange multipliers solving
the two point problem by adapting the search intervals according to the unsmooth shape of the augmented cost function. 相似文献
14.
J.-B. Caillau B. Daoud J. Gergaud 《Celestial Mechanics and Dynamical Astronomy》2012,114(1-2):137-150
The circular restricted three-body problem is considered to model the dynamics of an artificial body submitted to the attraction of two planets. Minimization of the fuel consumption of the spacecraft during the transfer, e.g. from the Earth to the Moon, is considered. In the light of the controllability results of Caillau and Daoud (SIAM J Control Optim, 2012), existence for this optimal control problem is discussed under simplifying assumptions. Thanks to Pontryagin maximum principle, the properties of fuel minimizing controls is detailed, revealing a bang-bang structure which is typical of L1-minimization problems. Because of the resulting non-smoothness of the Hamiltonian two-point boundary value problem, it is difficult to use shooting methods to compute numerical solutions (even with multiple shooting, as many switchings on the control occur when low thrusts are considered). To overcome these difficulties, two homotopies are introduced: One connects the investigated problem to the minimization of the L2-norm of the control, while the other introduces an interior penalization in the form of a logarithmic barrier. The combination of shooting with these continuation procedures allows to compute fuel optimal transfers for medium or low thrusts in the Earth–Moon system from a geostationary orbit, either towards the L 1 Lagrange point or towards a circular orbit around the Moon. To ensure local optimality of the computed trajectories, second order conditions are evaluated using conjugate point tests. 相似文献
15.
Troy A. Henderson John L. Junkins Gianmarco Radice 《Celestial Mechanics and Dynamical Astronomy》2009,104(4):355-368
A complex exponential solution has been derived which unifies the elliptic and hyperbolic trajectories into a single set of
equations and provides an exact, analytical solution to the unperturbed, Keplerian two-body problem. The formulation eliminates
singularities associated with the elliptic and hyperbolic trajectories that arise from these orbits. Using this complex exponential
solution formulation, a variation of parameters formulation for the perturbed two-body problem has been derived. In this paper,
we present the analytical formulation of the complex exponential solution, numerical simulations, a comparison with classical
solution methods, and highlight the benefits of this approach compared with the classical developments.
Previously presented as AAS 07-136 at the 17th AAS/AIAA Spaceflight Mechanics Meeting Sedona, Arizona, AAS 08-206 and AAS
08-230 at the 18th AAS/AIAA Spaceflight Mechanics Meeting Galveston, Texas. 相似文献
16.
17.
A new approach is presented for the problem of planar optimal impulsive rendezvous of a spacecraft in an inertial frame near
a circular orbit in a Newtonian gravitational field. The total characteristic velocity to be minimized is replaced by a related
characteristic-value function and this related optimization problem can be solved in closed form. The solution of this problem
is shown to approach the solution of the original problem in the limit as the boundary conditions approach those of a circular
orbit. Using a form of primer-vector theory the problem is formulated in a way that leads to relatively easy calculation of
the optimal velocity increments. A certain vector that can easily be calculated from the boundary conditions determines the
number of impulses required for solution of the optimization problem and also is useful in the computation of these velocity
increments. Necessary and sufficient conditions for boundary conditions to require exactly three nonsingular non-degenerate
impulses for solution of the related optimal rendezvous problem, and a means of calculating these velocity increments are
presented. A simple example of a three-impulse rendezvous problem is solved and the resulting trajectory is depicted. Optimal
non-degenerate nonsingular two-impulse rendezvous for the related problem is found to consist of four categories of solutions
depending on the four ways the primer vector locus intersects the unit circle. Necessary and sufficient conditions for each
category of solutions are presented. The region of the boundary values that admit each category of solutions of the related
problem are found, and in each case a closed-form solution of the optimal velocity increments is presented. Similar results
are presented for the simpler optimal rendezvous that require only one-impulse. For brevity degenerate and singular solutions
are not discussed in detail, but should be presented in a following study. Although this approach is thought to provide simpler
computations than existing methods, its main contribution may be in establishing a new approach to the more general problem. 相似文献
18.
The problem of designing low-energy transfers between the Earth and the Moon has attracted recently a major interest from the scientific community. In this paper, an indirect optimal control approach is used to determine minimum-fuel low-thrust transfers between a low Earth orbit and a Lunar orbit in the Sun–Earth–Moon Bicircular Restricted Four-Body Problem. First, the optimal control problem is formulated and its necessary optimality conditions are derived from Pontryagin’s Maximum Principle. Then, two different solution methods are proposed to overcome the numerical difficulties arising from the huge sensitivity of the problem’s state and costate equations. The first one consists in the use of continuation techniques. The second one is based on a massive exploration of the set of unknown variables appearing in the optimality conditions. The dimension of the search space is reduced by considering adapted variables leading to a reduction of the computational time. The trajectories found are classified in several families according to their shape, transfer duration and fuel expenditure. Finally, an analysis based on the dynamical structure provided by the invariant manifolds of the two underlying Circular Restricted Three-Body Problems, Earth–Moon and Sun–Earth is presented leading to a physical interpretation of the different families of trajectories. 相似文献
19.
Ai-hua Zhou Qi-jun Fu He-qi Zhang Xin-dong Wang 《Chinese Astronomy and Astrophysics》1996,20(4):458-466
The observations of a microwave burst with multiple impulses on 1993 Oct 2, 073940–074100 UT are analysed. This event consists of multiple impulses superimposed on a slowly varying burst background. Our formula for coronal magnetic field diagnostics was used here for the first time to derive the field strength and information on the energetic electrons. The results are: 1) The mean spectral index of the impulsive component in the optically thin part is less than that of the slow background by 1 (a harder spectrum). The mean brightness temperature at 19.6 GHz of the former is 6 times that of the latter. 2) The mean magnetic strengths of the impulse and slow burst regions are 158 G and 531 G, respectively. The time variation in the slow burst region is saddle-shaped, being 50% lower in the middle than at the beginning and end. 3) The column density NL and number density N of energetic electrons in the impulsive component are 4% and 8% of those of the slow component, but the energy flux and emission coefficient are 100% and 800% greater. The two components appear to be produced by two different electron groups with different energy distributions in two different regions. 相似文献
20.
Non-Keplerian orbits for electric sails 总被引：1，自引：0，他引：1
Giovanni Mengali Alessandro A. Quarta 《Celestial Mechanics and Dynamical Astronomy》2009,105(1-3):179-195
An electric sail is capable of guaranteeing the fulfilment of a class of trajectories that would be otherwise unfeasible through conventional propulsion systems. In particular, the aim of this paper is to analyze the electric sail capabilities of generating a class of displaced non-Keplerian orbits, useful for the observation of the Sun’s polar regions. These orbits are characterized through their physical parameters (orbital period and solar distance) and the spacecraft propulsion capabilities. A comparison with a solar sail is made to highlight which of the two systems is more convenient for a given mission scenario. The optimal (minimum time) transfer trajectories towards the displaced orbits are found with an indirect approach. 相似文献