R.S. Ball published his “A Treatise on the Theory of Screws” in 1900. The finite screws he describes are clearly rigid body motions. Ball’s instantaneous screws are elements of the Lie algebra of the group SE(3), or more precisely rays in the Lie algebra. Although roughly contemporary with the work of Lie and Killing, Ball’s work had a rather different focus from the emerging theory of Lie groups and algebras. We hope to show the connections here. We begin by looking at Lie algebras in general.
KeywordsNormal Subgroup Tangent Vector Adjoint Representation Home Position Killing Form
Unable to display preview. Download preview PDF.