Skip to main content
SpringerLink
Log in

Generalized covariant derivative with respect to time in flat space (II): Lagrangian description

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Yin, Y.J., The generalized covariant derivative with respect to time in flat space (I): Eulerian description. Acta Mechanica Solida Sinica, 2016, 29(4): 345–358.

    Article  Google Scholar 

  2. Huang, K.C., Xue, M.D. and Lu, M.W., Tensor Analysis, 2nd edition. 2003, Tsinghua University Press.

  3. Yin, Y.J., Extension of covariant derivative (I): from component form to objective form. Acta Mechanica Sinica, 2015, 31(1): 79–87.

    Article  MathSciNet  Google Scholar 

  4. Yin, Y.J., Extension of covariant derivative (II): from flat space to curved space. Acta Mechanica Sinica, 2015, 31(1): 88–95.

    Article  MathSciNet  Google Scholar 

  5. Yin, Y.J., Extension of the covariant derivative (III): from classical gradient to shape gradient. Acta Mechanica Sinica, 2015, 31(1): 96–103.

    Article  MathSciNet  Google Scholar 

  6. Yin, Y.J., Generalized covariant differentiation and axiom-based tensor analysis. Applied Mathematics and Mechanics, English edition, 2016, 37(3): 379–394.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Yajun Yin

Authors
  1. Yajun Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

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). The author thanks Prof. Wu Jike for his fruitful discussions and suggestions.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yin, Y. Generalized covariant derivative with respect to time in flat space (II): Lagrangian description. Acta Mech. Solida Sin. 29, 359–370 (2016). https://doi.org/10.1016/S0894-9166(16)30239-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/S0894-9166(16)30239-7

Key Words

Search

Navigation