Abstract
A four dimensional treatment of nonrelativistic spacetime gives a natural frame to deal with objective time derivatives. In this framework some well known objective time derivatives of continuum mechanics appear as Lie derivatives. Their coordinatized forms depend on the tensorial properties of the relevant physical quantities. We calculate the particular forms of objective time derivatives for scalars, vectors, covectors, and different second order tensors from the point of view of a rotating observer. The relation of substantial, material, and objective time derivatives is treated.
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