The concept of objectivity in classical field theories is traditionally based
on time dependent Euclidean transformations. In this paper we treat objectivity
in a four-dimensional setting, calculate Christoffel symbols of the spacetime
transformations, and give covariant and material time derivatives. The usual
objective time derivatives are investigated.Comment: 6 pages, 1 figur
Exact and simple calculation of Thomas rotation and Thomas precessions along a circular world line is presented in an absolute (coordinatefree) formulation of special relativity. Besides the simplicity of calculations the absolute treatment of spacetime allows us to gain a deeper insight into the phenomena of Thomas rotation and Thomas precession.
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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