Lie groups, systems on groups, and symmetries
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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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