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Bounded motion design in the Earth zonal problem using differential algebra based normal form methods

Weisskopf, Adrian and Armellin, Roberto and Berz, Martin Bounded motion design in the Earth zonal problem using differential algebra based normal form methods. (2020) Celestial Mechanics and Dynamical Astronomy, 132 (14). 1-32. ISSN 0923-2958

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Official URL: https://doi.org/10.1007/s10569-020-9953-x

Abstract

Establishing long-term relative bounded motion between orbits in perturbed dynamics is a key challenge in astrodynamics to enable cluster flight with minimum propellant expenditure. In this work, we present an approach that allows for the design of long-term relative bounded motion considering a zonal gravitational model. Entire sets of orbits are obtained via high-order Taylor expansions of Poincarè return maps about reference fixed points. The high-order normal form algorithm is used to determine a change in expansion variables of the map into normal form space, in which the phase space behavior is circular and can be easily parameterized by action–angle coordinates. The action–angle representation of the normal form coordinates is then used to parameterize the original Poincarè return map and average it over a full phase space revolution by a path integral along the angle parameterization. As a result, the averaged nodal period and drift in the ascending node are obtained, for which the bounded motion conditions are straightforwardly imposed. Sets of highly accurate bounded orbits are obtained, extending over several thousand kilometers, and valid for decades.

Item Type:Article
HAL Id:hal-03100444
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Michigan State University - MSU (USA)
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Deposited On:06 Jan 2021 15:10

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