Exploitation of three-body dynamics in space mission design

Abstract

With renewed interest in space exploration, the question of designing efficient transfers between celestial bodies is as relevant as ever. Combined with the rise of scientific computing in the latter half of the 20th century, significant attention has been given to using modern computing methods to design more efficient orbital transfers to reduce costs and improve overall mission lifetime.
Preliminary mission design is often performed in simplified, time-independent models of motion. In these, classical dynamical systems theory identifies dynamical structures which can be used to create low-energy transfers between points in space, or used to create orbits that exist as a delicate balance of gravity to achieve mission objectives. However, in more realistic, time-dependent models such structures are not guaranteed to exist. Attention has thus been given to techniques well-developed in fluid dynamics to identify similar structures in astrodynamics systems, but numerical and computational difficulties have frustrated these efforts.

This PhD is separated into two parts. The first studies the use of time-independent dynamical structures in space mission design in combination with high-performance computing techniques. An intensive optimisation procedure is used to construct transfers that use the invariant manifolds to retrieve asteroids into two of the equilibrium points of the Sun-Earth system. This PhD improves on the state of the art in this field by improving the methods used to find and construct the retrieval transfers. As a result, 27 more asteroids that are considered ‘easily retrievable’ are found, and the velocity required to compute the transfers is generally reduced for those already considered easily retrievable. Moreover, it is revealed that these transfers exist across a range of transfer times, allowing greater flexibility for mission designers.

The second part of this thesis uses techniques from fluid mechanics to find analogous structures to those used in the asteroid retrieval study directly in time-dependent models of motion, rather than needing to use simplified models. This thesis makes two improvements to the current body of research: the first is the presentation of an improved numerical method to compute Lagrangian Coherent Structures (LCS) in three-dimensional dynamical systems called DA-LCS. This numerical method uses a direct computer implementation of an algebra of polynomials to compute more accurate and less numerically noisy quantities that signal LCS in general dynamical systems, and greatly outperforms standard approaches in astrodynamics systems. Since the relevant quantities are computed as polynomial expansions, the method also allows the computation of all relevant quantities completely automatically.
This numerical method is then applied to a series of test cases from astrodynamics, where three-dimensional LCS is constructed and shown to perform the role of generalised unstable manifolds in astrodynamics systems by separating qualitatively different behaviour. The effect of orbit parameterisation and integration time is also elaborated in an effort to provide the space community with in-depth knowledge of how to use LCS in astrodynamics in future studies.

More information

Identifiers

ORCID for Jack Tyler: orcid.org/0000-0002-0979-7533

ORCID for Alexander Wittig: orcid.org/0000-0002-4594-0368

Catalogue record

Export record