An introduction to differential algebra and the differential algebra manifold representation
An introduction to differential algebra and the differential algebra manifold representation
Differential Algebra techniques have been used extensively in the past decade to treat various problems in astrodynamics. In this paper we review the Differential Algebra technique and present four different views of the method. We begin with the introduction of the mathematical definition of the technique as a particular algebra of polynomials. We then give an interpretation of the computer implementation of the method as a way to represent function spaces on a computer, which naturally leads to a view of the method as an automatic differentiation technique. We then proceed to the set theoretical view of Differential Algebra for representing sets of points efficiently on a computer, which is of particular value in astrodynamics. After this introduction to the well known classical DA techniques, we introduce the concept of a DA manifold and show how they naturally arise as an extension of classical DA set propagation. A manifold propagator that allows the accurate propagation of large sets of initial conditions by means of automatic domain splitting (ADS) is described. Its function is illustrated by applying it to the propagation of a set of initial conditions in the two-body problem.
293-309
Kluwer Academic Publishers
Wittig, Alexander
3a140128-b118-4b8c-9856-a0d4f390b201
2016
Wittig, Alexander
3a140128-b118-4b8c-9856-a0d4f390b201
Wittig, Alexander
(2016)
An introduction to differential algebra and the differential algebra manifold representation.
In,
Gomez, G. and Masdemont, J.
(eds.)
Astrodynamics Network AstroNet-II - The Final Conference.
AstroNet-II International Final Conference, 2015 (15/06/15 - 19/06/15)
Kluwer Academic Publishers, .
(doi:10.1007/978-3-319-23986-6_20).
Record type:
Book Section
Abstract
Differential Algebra techniques have been used extensively in the past decade to treat various problems in astrodynamics. In this paper we review the Differential Algebra technique and present four different views of the method. We begin with the introduction of the mathematical definition of the technique as a particular algebra of polynomials. We then give an interpretation of the computer implementation of the method as a way to represent function spaces on a computer, which naturally leads to a view of the method as an automatic differentiation technique. We then proceed to the set theoretical view of Differential Algebra for representing sets of points efficiently on a computer, which is of particular value in astrodynamics. After this introduction to the well known classical DA techniques, we introduce the concept of a DA manifold and show how they naturally arise as an extension of classical DA set propagation. A manifold propagator that allows the accurate propagation of large sets of initial conditions by means of automatic domain splitting (ADS) is described. Its function is illustrated by applying it to the propagation of a set of initial conditions in the two-body problem.
This record has no associated files available for download.
More information
e-pub ahead of print date: 30 July 2016
Published date: 2016
Venue - Dates:
AstroNet-II International Final Conference, 2015, , Tossa de Mar, Spain, 2015-06-15 - 2015-06-19
Identifiers
Local EPrints ID: 419787
URI: http://eprints.soton.ac.uk/id/eprint/419787
PURE UUID: c5e80ddf-f28b-4529-b051-c17e3d998aa4
Catalogue record
Date deposited: 20 Apr 2018 16:30
Last modified: 06 Jun 2024 01:59
Export record
Altmetrics
Contributors
Editor:
G. Gomez
Editor:
J. Masdemont
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
