Closed form solution for p-curves in SO(4)

Carol Linton; William Holderbaum; James Biggs

Closed form solution for p-curves in SO(4)

Carol Linton, William Holderbaum, James Biggs

Mechanical And Aerospace Engineering

Research output: Contribution to conference › Paper › peer-review

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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.

Original language	English
Number of pages	6
Publication status	Published - Jun 2012
Event	American Control Conference - Montreal, Canada Duration: 27 Jun 2012 → 29 Jun 2012

Conference

Conference	American Control Conference
Country/Territory	Canada
City	Montreal
Period	27/06/12 → 29/06/12

Keywords

motion planning
p-curves in SO(4)
Casimir invariants and Lax operators
double cover isomorphism

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Biggs JD Pure Closed form solution for p curves in SO 4 Jul 2012Submitted manuscript, 533 KB

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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 isprovided, 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 isgeneric and can be applied to other problems.",

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N2 - 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 isprovided, 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 isgeneric and can be applied to other problems.

AB - 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 isprovided, 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 isgeneric and can be applied to other problems.

KW - motion planning

KW - p-curves in SO(4)

KW - Casimir invariants and Lax operators

KW - double cover isomorphism

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M3 - Paper

T2 - American Control Conference

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ER -

Closed form solution for p-curves in SO(4)

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Keywords

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