Physical and Anholonomic Components of Tensors via Invariance of the Tensor Representation

Abstract

This article is concerned with the theory of physical and anholonomic components of tensors of single and double field based on the method of invariance of the tensor representation. It obtains formulas that describe a more general tensor calculus, which includes, as a particular case, the tensor calculus based on coordinate transformation. Explicit expressions of the usual connections are obtained from a study of the anholonomic connections. Also, expressions of the anholonomic components of the covariant derivative of a tensor are provided. As an application of this theory, the nonlinear kinematic equations of a body are written in terms of anholonomic components.