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Self-scaling Collocation Methods Preserving Constants of Motion

Sagliano, Marco and Hölzel, Matthew (2021) Self-scaling Collocation Methods Preserving Constants of Motion. In: AIAA Scitech 2021 Forum. AIAA SciTech Forum and Exposition 2021, 11-22 January 2021, Virtual Event. doi: 10.2514/6.2021-0285. ISBN 978-162410609-5.

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Official URL: https://arc.aiaa.org/doi/10.2514/6.2021-0285

Abstract

We present a class of self-scaling collocation integrators which, unlike explicit Runge-Kutta integrators, will automatically preserve quadratic constants of motion such as energy,linear momentum, and angular momentum, without the need for small stepsizes. However,collocation integrators in general require numerical optimization to solve an implicit set ofequations which are difficult and computationally expensive to solve when the problem’s Ja-cobian becomes ill-conditioned. Therefore, the integrators we present automatically scale thecollocation conditions using a generalized eigenvalue problem (GEVP) approach, and exploitthe Jacobian’s structure to improve the optimization algorithm’s precision and speed. Nu-merical results show that the presented integrators preserve invariants in a broader class ofintegration problems, with an improvement of approximately one order of magnitude overtraditional Runge-Kutta 4(5) schemes.

Item URL in elib:https://elib.dlr.de/140560/
Document Type:Conference or Workshop Item (Speech)
Title:Self-scaling Collocation Methods Preserving Constants of Motion
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Sagliano, Marcomarco.sagliano (at) dlr.dehttps://orcid.org/0000-0003-1026-0693
Hölzel, Matthewhoelzel (at) uni-bremen.dehttps://orcid.org/0000-0002-6200-4600
Date:12 January 2021
Journal or Publication Title:AIAA Scitech 2021 Forum
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:No
DOI :10.2514/6.2021-0285
ISBN:978-162410609-5
Status:Published
Keywords:Collocation methods, implicit integrators, Runge-Kutta integrators, Optimization, Self-scaling, Hybrid Jacobian, Complex-Step, Orbital Propagator, Quadratic Constants
Event Title:AIAA SciTech Forum and Exposition 2021
Event Location:Virtual Event
Event Type:international Conference
Event Dates:11-22 January 2021
Organizer:AIAA
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space Exploration
DLR - Research area:Raumfahrt
DLR - Program:R EW - Space Exploration
DLR - Research theme (Project):R - Vorhaben Landetechnologien (old)
Location: Bremen
Institutes and Institutions:Institute of Space Systems > Navigation and Control Systems
Deposited By: Sagliano, Marco
Deposited On:20 Jan 2021 09:39
Last Modified:08 Feb 2021 12:21

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