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Generalized covariant derivative with respect to time in flat space (I): Eulerian description

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Abstract

This paper reports a new derivative in the Eulerian description in flat space-the generalized covariant derivative with respect to time. The following contents are included: (a) the restricted covariant derivative with respect to time for Eulerian component is defined; (b) the postulate of the covariant form invariability in time field is set up; (c) the generalized covariant derivative with respect to time for generalized Eulerian component is defined; (d) the algebraic structure of the generalized covariant derivative with respect to time is made clear; (e) the covariant differential transformation group in time filed is derived. These progresses reveal the covariant form invariability of Eulerian space and time.

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Authors and Affiliations

  1. Department of Engineering Mechanics, School of Aerospace Engineering, Tsinghua University, 100084, Beijing, China

    Yajun Yin

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  1. Yajun Yin
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Correspondence to Yajun Yin.

Additional information

Project supported by the National Natural Sciences Foundation of China (No. 11272175) and the Specialized Research Found for Doctoral Program of Higher Education (No. 20130002110044).

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Yin, Y. Generalized covariant derivative with respect to time in flat space (I): Eulerian description. Acta Mech. Solida Sin. 29, 345–358 (2016). https://doi.org/10.1016/S0894-9166(16)30238-5

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  • DOI: https://doi.org/10.1016/S0894-9166(16)30238-5

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