Abstract
Frame bundles are described with respect to their role in continuum mechanics, the structure jet groups are studied and some expressions in local coordinates are derived. It is introduced the general (r-th order) microstructure configuration and it is suggested what needs to be investigated in subsequent research.
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- 1.
In classical situations, we meet the case \(\dim B\le 3\) and \(S=\mathbb R^3\) where B can be covered by a single map, so both index set I and \(\bar{I}\) are singleton. Let us mention as a curiosity that some authors, cf. [5], consider local maps inversely—as mappings from the real space to a manifold, which is not a problem.
- 2.
thus not depending on \(\xi ^j_{\bar{j}}\).
- 3.
such a group homomorphisms can be induced by an action (left or right) of \(\bar{H}\) on \(\bar{N}\), for details see [6].
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Acknowledgments
The research is supported by Brno University of Technology, the specific research plan No. FSI-S-14-2290.
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Kureš, M. (2016). Some Remarks to Higher Order Frames Occurring in Continuum Mechanics. In: Albers, B., Kuczma, M. (eds) Continuous Media with Microstructure 2. Springer, Cham. https://doi.org/10.1007/978-3-319-28241-1_4
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DOI: https://doi.org/10.1007/978-3-319-28241-1_4
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