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Generalized Covariant Derivative with Respect to Time in Flat Space(Ⅰ):Eulerian Description 被引量:2
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作者 Yajun Yin 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2016年第4期345-358,共14页
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... 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. 展开更多
关键词 Eulerian description covariant form invariability generalized Eulerian component generalized covariant derivative with respect to time covariant differential transformation group
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Generalized Covariant Derivative with Respect to Time in Flat Space(Ⅱ):Lagrangian Description 被引量:2
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作者 Yajun Yin 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2016年第4期359-370,共12页
The previous paper reported a new derivative in the Eulerian description in flat space—the generalized covariant derivative of generalized Eulerian component with respect to time. This paper extends the thought from ... The previous paper reported a new derivative in the Eulerian description in flat space—the generalized covariant derivative of generalized Eulerian component with respect to time. This paper extends the thought from the Eulerian description to the Lagrangian description:on the basis of the postulate of covariant form invariability in time field, we define a new derivative in the Lagrangian description in flat space—the generalized covariant derivative of generalized Lagrangian component with respect to time. Besides, the covariant differential transformation group is set up. The covariant form invariability of Lagrangian space-time is ascertained. 展开更多
关键词 Lagrangian description the postulate of covariant form invariability generalized Lagrangian component generalized covariant derivative with respect to time covariant differential transformation group
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