The Applications of lie algebra to the spatial motions

ABSTRACT The oriented lines in Euclidean space ( R^ ) are in one-to-one correspondence with the points of the dual unit sphere in dual space ( D3 ). Lie Algebra and module over the dual number ring endowed with a dual valued inner product. We use the Campbell-Hausdorf formula of Lie's general theory. The Campbell-Hausdorf formula is used for the consecutive motion. In this work, the motion of a point on dual sphere is given by Olinde-Rodrigues formula and also infinitesimal motion of this motion and high degree of acceleration of velocity are calculated. Moreover it is defined with respect to lie bracket.