Formalization of Technological Processes Based on Vector and Tensor Analysis

Authors

DOI:

https://doi.org/10.20535/2521-1943.2025.9.4(107).341433

Keywords:

vector, tensor, basis, Kronecker symbol, scalar product, cosine similarity, ADS, CTS, TP, PCM

Abstract

The work further develops the results of studies [1]–[5] based on a systematic analysis using an interpretative-formal approach in a new scientific and technical direction – the technological interpretation of provisions of vector and tensor analysis that are similar in meaning. This allows expanding the formal field of representation of technological processes within the concept of their “technological meaning” and increasing the formal capacity of TP description. The results of research are revealed in the practical and production aspects related to TP, providing for the application of vector and tensor analysis in the coordinate approach, technological space, scalar product, matrix tensor, as well as examples of tensor and vector analysis in composite AKZ technology. It is determined that vectors (tensors) can be specified in different ways, depending on the technological context (polymer composite materials technology – PCM), and the set of components is only its representation in a certain (in terms of detail) basis. A coordinate approach is used, as well as the possibility of other methods of specifying and working with vectors (tensors) using the example of ordinary vectors and simple second-rank tensors, characterized by the powerful idea of orthogonality. Since the second vector and tensor represent real technological objects, including: autonomous dynamic systems (ADS), structural and technological solutions (STS), technological processes (TP), in the form of contravariant and covariant vectors, etc.
The interpretative correspondence of the technological interpretation of contravariant and covariant coordinates of a vector is shown, and the nature of the relationships between technological contravariant and technological covariant coordinates is established.
The example demonstrates the invariance of the enlarged stages of a complex technological process in different coordinate systems, which confirms the invariance of the technological vector under the condition of transformation of its coordinates.

References

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Published

2025-12-29

How to Cite

[1]
V. Zabashta, “Formalization of Technological Processes Based on Vector and Tensor Analysis”, Mech. Adv. Technol., vol. 9, no. 4(107), pp. 456–468, Dec. 2025.

Issue

Vol. 9 No. 4(107) (2025)

Section

Aviation Systems and Technologies

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Copyright (c) 2025 Володимир Забашта

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