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Density evolution of high area-to-mass objects using semi-analytical and differential algebra techniques

Density evolution of high area-to-mass objects using semi-analytical and differential algebra techniques
Density evolution of high area-to-mass objects using semi-analytical and differential algebra techniques

This paper introduces and combines two novel techniques. Firstly, we introduce an efficient numerical method for the propagation of entire sets of initial conditions in the phase space and their associated phase space densities based on Differential Algebra (DA) techniques. Secondly, this DA density propagator is applied to a DA-enabled implementation of Semi-Analytical (SA) averaged dynamics, combining for the first time the power of the SA and DA techniques. While the DA-based method for the propagation of densities introduced in this paper is independent of the dynamical system under consideration, the particular combination of DA techniques with SA equations yields a fast and accurate method to propagate large clouds of initial conditions and their associated probability density functions very efficiently for long time. This enables the study of the long-term behavior of particles subjected to the given dynamics. To demonstrate the effectiveness of the proposed method, the evolution of a cloud of high area-to-mass objects in Medium Earth Orbit is reproduced considering the effects of solar radiation pressure, the Earth's oblateness and luni-solar perturbations. The computational efficiency is demonstrated by propagating 10.000 random samples taking snapshots of their state and density at evenly spaced intervals throughout the integration. The total time required for a propagation for 16 years in the dynamics is on the order of tens of seconds on a common desktop PC.

4599-4609
International Astronautical Federation, IAF
Wittig, Alexander
3a140128-b118-4b8c-9856-a0d4f390b201
Colombo, Camilla
595ced96-9494-40f2-9763-ad4a0f96bc86
Armellin, Roberto
61950d5c-3dcf-45f5-b391-7e8c6ffb8e6f
Wittig, Alexander
3a140128-b118-4b8c-9856-a0d4f390b201
Colombo, Camilla
595ced96-9494-40f2-9763-ad4a0f96bc86
Armellin, Roberto
61950d5c-3dcf-45f5-b391-7e8c6ffb8e6f

Wittig, Alexander, Colombo, Camilla and Armellin, Roberto (2014) Density evolution of high area-to-mass objects using semi-analytical and differential algebra techniques. In 65th International Astronautical Congress 2014, IAC 2014: Our World Needs Space. vol. 7, International Astronautical Federation, IAF. pp. 4599-4609 .

Record type: Conference or Workshop Item (Paper)

Abstract

This paper introduces and combines two novel techniques. Firstly, we introduce an efficient numerical method for the propagation of entire sets of initial conditions in the phase space and their associated phase space densities based on Differential Algebra (DA) techniques. Secondly, this DA density propagator is applied to a DA-enabled implementation of Semi-Analytical (SA) averaged dynamics, combining for the first time the power of the SA and DA techniques. While the DA-based method for the propagation of densities introduced in this paper is independent of the dynamical system under consideration, the particular combination of DA techniques with SA equations yields a fast and accurate method to propagate large clouds of initial conditions and their associated probability density functions very efficiently for long time. This enables the study of the long-term behavior of particles subjected to the given dynamics. To demonstrate the effectiveness of the proposed method, the evolution of a cloud of high area-to-mass objects in Medium Earth Orbit is reproduced considering the effects of solar radiation pressure, the Earth's oblateness and luni-solar perturbations. The computational efficiency is demonstrated by propagating 10.000 random samples taking snapshots of their state and density at evenly spaced intervals throughout the integration. The total time required for a propagation for 16 years in the dynamics is on the order of tens of seconds on a common desktop PC.

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More information

Published date: 2014
Venue - Dates: 65th International Astronautical Congress 2014: Our World Needs Space, IAC 2014, Toronto, Canada, 2014-09-29 - 2014-10-03

Identifiers

Local EPrints ID: 419782
URI: http://eprints.soton.ac.uk/id/eprint/419782
PURE UUID: 902e04af-3bd8-4752-bf6b-1a52afb17700
ORCID for Alexander Wittig: ORCID iD orcid.org/0000-0002-4594-0368
ORCID for Camilla Colombo: ORCID iD orcid.org/0000-0001-9636-9360

Catalogue record

Date deposited: 20 Apr 2018 16:30
Last modified: 20 Jul 2019 01:33

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