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High order expansion of the solution of two-point boundary value problems using differential algebra: applications to spacecraft dynamics

Di Lizia, P, Armellin, R, Bernelli Zazzera, F and Berz, M (2008) High order expansion of the solution of two-point boundary value problems using differential algebra: applications to spacecraft dynamics In: 5th International Workshop on Taylor Model Methods, 2008-05-20 - 2008-05-23, Fields Institute for Research in Mathematical Science in Toronto, Canada.

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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. However, a certain level of approximation always affects the dynamical models adopted to design the nominal trajectory of a spacecraft. Dynamical perturbations usually act on the spacecraft in real scenarios, deviating it from the desired nominal trajectory. Conse- quently, the boundary conditions assumed for the nominal solutions are usually affected by uncertainties and errors. Suitable techniques must be developed to quickly compute correction maneuvers to compensate for such errors in practical applications. This work proposes differential algebra as a valuable tool to face the previous problem. An algorithm is presented, which is able to deliver the arbitrary order Taylor expansion of the solution of a two-point boundary value problem about an available nominal solution. The mere evaluation of the resulting polynomials en- ables the design of the desired correction maneuvers. The performances of the algorithm are assessed by addressing typical applications in the field of spacecraft dynamics, such as the simple Lambert’s problem and the station keeping of a spacecraft around a nominal halo orbit.

Item Type: Conference or Workshop Item (Conference Paper)
Subjects : Electronic Engineering
Divisions : Faculty of Engineering and Physical Sciences > Electronic Engineering
Authors :
AuthorsEmailORCID
Di Lizia, PUNSPECIFIEDUNSPECIFIED
Armellin, RUNSPECIFIEDUNSPECIFIED
Bernelli Zazzera, FUNSPECIFIEDUNSPECIFIED
Berz, MUNSPECIFIEDUNSPECIFIED
Date : 20 May 2008
Contributors :
ContributionNameEmailORCID
PublisherAmerican Mathematical Society, UNSPECIFIEDUNSPECIFIED
Depositing User : Symplectic Elements
Date Deposited : 11 Jan 2017 10:17
Last Modified : 11 Jan 2017 10:17
URI: http://epubs.surrey.ac.uk/id/eprint/813261

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