Absolute Time Derivatives

Details Absolute Time Derivatives Absolute Time Derivatives

2006-08-31

arxiv.org/abs/math-ph/0608065v2

Journal of Mathematical Physics, 2007, V48, 053507-19.

Physics

Mathematical Physics

26 pages, 4 figures (minor revision)

Scientific paper

10.1063/1.2719144

A four dimensional treatment of nonrelativistic space-time 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 depends 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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