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

Carol Linton, William Holderbaum, James Biggs

Research output: Contribution to conferencePaperpeer-review

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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 languageEnglish
Number of pages6
Publication statusPublished - Jun 2012
EventAmerican Control Conference - Montreal, Canada
Duration: 27 Jun 201229 Jun 2012


ConferenceAmerican Control Conference


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


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