- Title
- Control and integrability on SO (3)
- Creator
- Remsing, C C
- Date
- 2010
- Type
- Article
- Identifier
- vital:6787
- Identifier
- http://hdl.handle.net/10962/d1006938
- Description
- This paper considers control ane left- invariant systems evolving on matrix Lie groups. Such systems have signicant applications in a variety of elds. Any left-invariant optimal control problem (with quadratic cost) can be lifted, via the celebrated Maximum Principle, to a Hamiltonian system on the dual of the Lie algebra of the underlying state space G. The (minus) Lie-Poisson structure on the dual space g is used to describe the (normal) extremal curves. An interesting, and rather typical, single-input con- trol system on the rotation group SO (3) is investi- gated in some detail. The reduced Hamilton equa- tions associated with an extremal curve are derived in a simple and elegant manner. Finally, these equations are explicitly integrated by Jacobi elliptic functions.
- Format
- 6 pages, pdf
- Language
- English
- Relation
- Remsing, C.C. (2010) Control and Integrability on SO (3). Lecture Notes in Engineering and Computer Science, 2185 (1). pp. 1705-1710.
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Collections
Remsing, Claudiu C (Dr)
RU Department of Mathematics (Pure and Applied)
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