DEFORMATION OF TENSOR FIELDS DESCRIBED BY TIME-DEPENDENT MAPPINGS

This paper deals with tensor fields that are in some way attached to a deforming body. A meaningful characterization of the variation in time of a vector attached to a certain particle requires a reduction of the involved comparison of vectors in different places and times to a comparison of vectors at the same place and time. This is achieved here by means of an entrained vector, obeying some entrainment law specific to the type of vector. The direct method of description employed throughout the paper is intended to bring out directly the geometrical contents of both arguments and results. The charts involved may be obtained by time-dependent mapping procedures and need not stand in a prescribed relation to the entrainment law. The connection between entrainment law and convective derivative for tensorial compositions simultaneously involving various entrainment types has been developed in detail. © 1969 Springer-Verlag.