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Application of high order expansions of two-point boundary value problems to astrodynamics

Application of high order expansions of two-point boundary value problems to astrodynamics
Application of high order expansions of two-point boundary value problems to astrodynamics
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.
two-point boundary value problem, differential algebra, halo orbit, aerocapture
0923-2958
355-375
Di Lizia, P.
0f45735c-5c72-418f-945d-a5688f10c71e
Armellin, R.
61950d5c-3dcf-45f5-b391-7e8c6ffb8e6f
Lavagna, M.
3741b245-5b67-4371-b539-e9ba65e6c862
Di Lizia, P.
0f45735c-5c72-418f-945d-a5688f10c71e
Armellin, R.
61950d5c-3dcf-45f5-b391-7e8c6ffb8e6f
Lavagna, M.
3741b245-5b67-4371-b539-e9ba65e6c862

Di Lizia, P., Armellin, R. and Lavagna, M. (2008) Application of high order expansions of two-point boundary value problems to astrodynamics. Celestial Mechanics and Dynamical Astronomy, 102 (4), 355-375. (doi:10.1007/s10569-008-9170-5).

Record type: Article

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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More information

Published date: 1 December 2008
Keywords: two-point boundary value problem, differential algebra, halo orbit, aerocapture
Organisations: Aeronautics, Astronautics & Comp. Eng

Identifiers

Local EPrints ID: 358466
URI: https://eprints.soton.ac.uk/id/eprint/358466
ISSN: 0923-2958
PURE UUID: 19d38fc7-d4b3-4682-a547-dc2aa0b869a8

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Date deposited: 07 Oct 2013 11:06
Last modified: 18 Jul 2017 03:29

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