Baker-Campbell-Hausdorff-Dynkin formula for the lie algebra of rigid body displacements

Abstract

The paper proposes, for the first time, a closed form of the Baker-Campbell-Hausdorff-Dynkin (BCHD) formula in the particular case of the Lie algebra of rigid body displacements. For this purpose, the structure of the Lie group of the rigid body displacements SE(3) and the properties of its Lie algebra se(3) are used. In addition, a new solution to this problem in dual Lie algebra of dual vectors is delivered using the isomorphismbetween the Lie group SE(3) and the Lie group of the orthogonal dual tensors.