Generalized Integral Theorems and Application to the Equations of Continuum Mechanics

Autor:	M. K. Myers
Rok vydání:	2015
Předmět:	Discontinuity (linguistics) Generalized function Development (topology) Acoustics and Ultrasonics Continuum mechanics Generalized forces Quantum mechanics Structure (category theory) Aerospace Engineering Reynolds transport theorem Functional approach Applied mathematics Mathematics
Zdroj:	International Journal of Aeroacoustics. 14:1-24
ISSN:	2048-4003 1475-472X
DOI:	10.1260/1475-472x.14.1-2.1
Popis:	A development of generalized differentiation with respect to time is given within the structure of the functional approach to generalized function theory. The analysis is in parallel with techniques used in an earlier publication by F. Farassat and the author. The results are used to derive a generalized three dimensional Leibnitz' theorem that leads to a generalized Reynolds' transport theorem. This is then applied to derive the governing equations of continuum mechanics. It is shown that the process produces both the governing field equations and their associated discontinuity conditions in a single operation.
Databáze:	OpenAIRE
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