Lie groups, systems on groups, and symmetries

  • Francesco Bullo
  • Andrew D. Lewis
Part of the Texts in Applied Mathematics book series (TAM, volume 49)


The previous chapter provides a general framework for modeling mechanical control systems on manifolds. Frequently however, there is additional structure in a mechanical system that can be exploited for analysis and control. This chapter discusses an important class of manifolds, called Lie groups, that arise naturally in rigid body kinematics, as well as the properties of mechanical systems defined on Lie groups or possessing Lie group symmetries.


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Copyright information

© Springer Science+Business Media New York 2005

Authors and Affiliations

  • Francesco Bullo
    • 1
  • Andrew D. Lewis
    • 2
  1. 1.Department of Mechanical & Environmental EngineeringUniversity of California at Santa BarbaraSanta BarbaraUSA
  2. 2.Department of Mathematics and StatisticsQueen’s UniversityKingstonCanada

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