Abstract

In this paper, we provide a brief analysis of second-order skew-symmetric Cartesian tensors and present some of their applications in the analysis of spatial rotations. In particular by exploring various relationships between second-order skew-symmetric Cartesian tensors and their vector invariants, we provide a number of important tensor identities which enable us to manipulate effectively (and thus simplify) other complex tensor equations. Also, based on relatively oriented skew-symmetric second-order Cartesian tensors, we provide an analysis for the orientations of spatial rotations and derive some important formulations for their axes and the angles of rotation.

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