Linton, Carol and Holderbaum, William and Biggs, James (2012) Closed form solution for p-curves in SO(4). In: American Control Conference, 2012-06-27 - 2012-06-29.
Biggs_JD_Pure_Closed_form_solution_for_p_curves_in_SO_4_Jul_2012.pdf - Preprint
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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.
|Item type:||Conference or Workshop Item (Paper)|
|Keywords:||motion planning, p-curves in SO(4), Casimir invariants and Lax operators, double cover isomorphism, Mechanical engineering and machinery, Motor vehicles. Aeronautics. Astronautics, Aerospace Engineering|
|Subjects:||Technology > Mechanical engineering and machinery
Technology > Motor vehicles. Aeronautics. Astronautics
|Department:||Faculty of Engineering > Mechanical and Aerospace Engineering
Technology and Innovation Centre > Advanced Engineering and Manufacturing
|Depositing user:||Pure Administrator|
|Date Deposited:||20 Feb 2012 12:25|
|Last modified:||07 Jan 2017 22:14|