### 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.

Original language | English |
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Article number | 053507 |

Journal | Journal of Mathematical Physics |

Volume | 48 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2007 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*48*(5), [053507]. https://doi.org/10.1063/1.2719144

**Absolute time derivatives.** / Matolcsi, T.; Ván, P.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 48, no. 5, 053507. https://doi.org/10.1063/1.2719144

}

TY - JOUR

T1 - Absolute time derivatives

AU - Matolcsi, T.

AU - Ván, P.

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34249913933&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249913933&partnerID=8YFLogxK

U2 - 10.1063/1.2719144

DO - 10.1063/1.2719144

M3 - Article

AN - SCOPUS:34249913933

VL - 48

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 5

M1 - 053507

ER -