DocumentCode
574084
Title
Closed form solution for p-curves in SO(4)
Author
Linton, C. ; Holderbaum, William ; Biggs, James
Author_Institution
Sch. of Syst. Eng., Univ. of Reading, Reading, UK
fYear
2012
fDate
27-29 June 2012
Firstpage
226
Lastpage
231
Abstract
This paper describes the solution for p-curves in SO(4) and gives its closed form. The rotational symmetry was exploited in order to simplify the algebra. The relationship between the Casimir invariant functions and Lax operator is provided, along with its use as part of a Lax pair. The double cover by SU(2) × SU(2) enables two simpler problems to be found and integrated using Philip Hall coordinates and the solutions are then projected onto SO(4). The methodology is generic and can be applied to other problems.
Keywords
Lie algebras; SO(4) groups; SU(2) theory; differential equations; path planning; Casimir invariant functions; Lax operator; Lax pair; Philip Hall coordinates; SO(4); SU(2)×SU(2) double cover; algebra; closed form solution; p-curve solution; rotational symmetry; Aerospace electronics; Educational institutions; Electronic mail; Equations; Planning; Vectors; Casimir invariants and Lax operators; Motion planning; double cover isomorphism; p-curves in SO(4);
fLanguage
English
Publisher
ieee
Conference_Titel
American Control Conference (ACC), 2012
Conference_Location
Montreal, QC
ISSN
0743-1619
Print_ISBN
978-1-4577-1095-7
Electronic_ISBN
0743-1619
Type
conf
DOI
10.1109/ACC.2012.6314667
Filename
6314667
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