Embedded geodesic problems and optimal control for matrix lie groups

Anthony M. Bloch, Peter E. Crouch, Nikolaj Nordkvist, Amit Sanyal

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

This paper is devoted to a detailed analysis of the geodesic problem on matrix Lie groups, with left invariant metric, by examining representations of embeddings of geodesic ows in suitable vector spaces. We show how these representations generate extremals for optimal control problems. In particular we discuss in detail the symmetric representation of the so-called n-dimensional rigid body equation and its relation to the more classical Euler description. We detail invariant manifolds of these ows on which we are able to define a strict notion of equivalence between representations, and identify naturally induced symplectic structures.

Original languageEnglish (US)
Pages (from-to)197-223
Number of pages27
JournalJournal of Geometric Mechanics
Volume3
Issue number2
DOIs
StatePublished - Jun 1 2011
Externally publishedYes

Fingerprint

Lie groups
Matrix Groups
Vector spaces
Geodesic
Optimal Control
Invariant Metric
Symplectic Structure
Invariant Manifolds
Rigid Body
Vector space
Euler
Optimal Control Problem
n-dimensional
Equivalence

Keywords

  • Generalized rigid body mechanics
  • Geodesics
  • Optimal control

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization
  • Geometry and Topology
  • Mechanics of Materials

Cite this

Embedded geodesic problems and optimal control for matrix lie groups. / Bloch, Anthony M.; Crouch, Peter E.; Nordkvist, Nikolaj; Sanyal, Amit.

In: Journal of Geometric Mechanics, Vol. 3, No. 2, 01.06.2011, p. 197-223.

Research output: Contribution to journalArticle

Bloch, Anthony M. ; Crouch, Peter E. ; Nordkvist, Nikolaj ; Sanyal, Amit. / Embedded geodesic problems and optimal control for matrix lie groups. In: Journal of Geometric Mechanics. 2011 ; Vol. 3, No. 2. pp. 197-223.
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