Embedded geodesic problems and optimal control for matrix lie groups

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

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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
Issue number2
StatePublished - Jun 2011
Externally publishedYes


  • Generalized rigid body mechanics
  • Geodesics
  • Optimal control

ASJC Scopus subject areas

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


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