Application of high order expansions of two-point boundary value problems to astrodynamics |
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Authors: | P Di Lizia R Armellin M Lavagna |
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Institution: | (1) Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via La Masa, 34, 20156 Milano, Italy |
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Abstract: | 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. |
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Keywords: | Two-point boundary value problem Differential algebra Halo orbit Aerocapture |
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