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Roberto Armellin Pierluigi Di Lizia Michele Lavagna 《Celestial Mechanics and Dynamical Astronomy》2012,112(3):331-352
A method for high-order treatment of uncertainties in preliminary orbit determination is presented. The observations consist
in three couples of topocentric right ascensions and declinations at three observation epochs. The goal of preliminary orbit
determination is to compute a trajectory that fits with the observations in two-body dynamics. The uncertainties of the observations
are usually mapped to the phase space only when additional observations are available and a least squares fitting problem
is set up. A method based on Taylor differential algebra for the analytical treatment of observation uncertainties is implemented.
Taylor differential algebra allows for the efficient computation of the arbitrary order Taylor expansion of a sufficiently
continuous multivariate function. This enables the mapping of the uncertainties from the observation space to the phase space
as high-order multivariate Taylor polynomials. These maps can then be propagated forward in time to predict the observable
set at successive epochs. This method can be suitably used to recover newly discovered objects when a scarce number of measurements
is available. Simulated topocentric observations of asteroids on realistic orbits are used to assess the performances of the
method. 相似文献
2.
Two-point boundary value problems appear frequently in space trajectory design. A remarkable example is represented by the
Lambert’s problem, where the conic arc linking two fixed positions in space in a given time is to be characterized in the
frame of the two-body problem. Classical methods to numerically solve these problems rely on iterative procedures, which turn
out to be computationally intensive in case of lack of good first guesses for the solution. An algorithm to obtain the high
order expansion of the solution of a two-point boundary value problem is presented in this paper. The classical iterative
procedures are applied to identify a reference solution. Then, differential algebra is used to expand the solution of the
problem around the achieved one. Consequently, the computation of new solutions in a relatively large neighborhood of the
reference one is reduced to the simple evaluation of polynomials. The performances of the method are assessed by addressing
typical applications in the field of spacecraft dynamics, such as the identification of halo orbits and the design of aerocapture
maneuvers. 相似文献
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R. Armellin P. Di Lizia F. Topputo M. Lavagna F. Bernelli-Zazzera M. Berz 《Celestial Mechanics and Dynamical Astronomy》2010,106(1):1-24
In this paper a differential algebra version of the gravity assist space pruning algorithm is presented. The use of differential
algebraic techniques is proposed to overcome the two main drawbacks of the existing algorithm, i.e., the steep increase of
the number of function evaluations with the number of planets involved in the transfer, and the use of a bounding procedure
that relies on Lipschitzian tolerances. Differential algebra allows us to process boxes in place of grid points, and to substitute
pointwise evaluations of the constraint functions with their Taylor expansions. Thanks to the particular instance of multi-gravity
assist problems dealt with, all the planet-to-planet legs can be treated independently, and forward and backward constraining
can be applied. The proposed method is applied to preprocess the search space of sample interplanetary transfers and it also
serves as a stepping stone towards a fully rigorous treatment of the pruning process based on Taylor models. 相似文献
4.
Fabio?FerrariEmail author Michèle?Lavagna Kathleen?C.?Howell 《Celestial Mechanics and Dynamical Astronomy》2016,125(4):413-433
The paper presents a strategy for trajectory design in the proximity of a binary asteroid pair. A novel patched approach has been used to design trajectories in the binary system, which is modeled by means of two different three-body systems. The model introduces some degrees of freedom with respect to a classical two-body approach and it is intended to model to higher accuracy the peculiar dynamical properties of such irregular and low gravity field bodies, while keeping the advantages of having a full analytical formulation and low computational cost required. The neighborhood of the asteroid couple is split into two regions of influence where two different three-body problems describe the dynamics of the spacecraft. These regions have been identified by introducing the concept of surface of equivalence (SOE), a three-dimensional surface that serves as boundary between the regions of influence of each dynamical model. A case of study is presented, in terms of potential scenario that may benefit of such an approach in solving its mission analysis. Cost-effective solutions to land a vehicle on the surface of a low gravity body are selected by generating Poincaré maps on the SOE, seeking intersections between stable and unstable manifolds of the two patched three-body systems. 相似文献
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R. Armellin M. Lavagna A. Ercoli-Finzi 《Celestial Mechanics and Dynamical Astronomy》2006,95(1-4):391-405
The aero-gravity assist maneuver is here proposed as a tool to improve the efficiency of the gravity assist as, thanks to the interaction with the planetary atmospheres, the angular deviation of the velocity vector can be definitely increased. Even though the drag reduces the spacecraft velocity, the overall Δυ gain could be remarkable whenever a high lift-to-drag vehicle is supposed to fly. Earlier studies offer simplified approaches according to both the dynamics modeling and the atmospheric trajectory constraints. In this paper a 3D dynamical model is adopted and a more realistic L/D performance for the hypersonic vehicle is assumed. Some relevant aspects related to the multidisciplinary design have been considered such as heating rates and structural loads bounding. Comparisons between in and out of plane maneuvering have been performed by assuming, as control variables, either the angle of attack or the bank angle, respectively. The optimal control problem has been solved by selecting a direct method approach. The dynamics has been transcribed into a set of non-linear constraints and the arising non-linear programming problem has been solved with a sequential quadratic programming solver. To gain the global optimum convergence the initial guess has been supplied by solving the same problem by a direct shooting technique and a genetic optimizer. 相似文献
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Celestial Mechanics and Dynamical Astronomy - We are dealing with the averaged model used to study the secular effects in the motion of a body of the negligible mass in the context of a spatial... 相似文献
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