On the Transposition Operators in a Generalised Vector and Tensor Calculus Scheme

Abstract

In previous papers [1], [2] and [3] we described the basic features of a generalized scheme of the vector and tensor calculus. In the present paper we investigate in detail the properties and role of the transposition operators in this scheme. In Chapter 1 the fundamentals of the scheme are described, while in Chapter 2 the basic properties of the transposition operators are established. In Chapter 3 the consequences of the required identical vanishing of the absolute differentials of the fundamental operator and of the transposition operators are investigated and the coefficients of connection are expressed in terms of the fundamental and transposition operator components. In Chapter 4 we discuss the role of the transposition operators in a space, i. e. their significance for the identification of the displacement vector components with the coordinate differentials and for the determination of the basis vector transformation coefficients. In Chapter 5 an important illustrative particular case of the scheme is considered.