ABSTRACT
For X ∈M3×3 we set for the deviatoric part dev X = X − 13 trX ∈sl(3), where sl(3) is the Liealgebra of traceless matrices. The set Sym(n) denotes all symmetric n × n-matrices. The Lie-algebra of so(3): ={X ∈ GL(3)|X T X =, det[X ] = 1} is given by the set so(3): ={X ∈M3×3|X T =−X } of all skew symmetric tensors. The canonical identification of so(3) and R3 is denoted by axl A ∈R3 for A ∈so(3). Note that (axlA) × ξ = A . ξ for all ξ ∈R3, such that Aij = ∑3k = 1 −εijk · axl Ak where εijk is the totally antisymmetric permutation tensor. Here, A · ξ denotes the application of the matrix A to the vector ξ and a × b is the usual cross-product.
